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Statistics homework help

Statistical Inferences

Regression Statistical Inference

Statistical Inferences

What types of inferences can we make?

• Estimate Y given value(s) of X

• Confidence limits on estimates of Y

• Prediction limits on estimates of Y

• Confidence limits on Slope parameter

Estimates of Y

How do we find estimates of Y given X?

Expected value of Y:

E{Y} = E{B0 + B1(X) + e}

since B0, B1, and X are constants…

E{Y} = B0 + B1(X) + E{e}

E{e}=0

So E{Y} = B0 + B1(X)

Just plug the value of X into the regression equation!

Confidence Limits of Y

How do we find confidence limits for estimates of Y?

It is similar to finding confidence limits of a sample mean

2-sided conf limits = E{Y} +/- tinv(%conf, Df) (s){conf}

1-sided lower conf = E{Y} – tinv(%conf, Df) (s){conf}

1-sided upper conf = E{Y} + tinv(%conf, Df) (s){conf}

where :

Df = degrees of freedom for the error term in the model = (n-p)

s{conf} = SQRT( MSE (1/n + (X-Xbar)^2/SSX))

X = value at which Y is to be estimated

Xbar = average of X values

SSX = sum(Xi-Xbar)^2

Confidence Limits of Y

In JASP, you can let the code do the work.

In Excel, you will have to calculate the s{conf} value in order to calculate the

confidence limits of Y.

Prediction Limits of Y

How do we find prediction limits for estimates of Y?

2-sided prediction limits = E{Y} +/- tinv(%conf, Df)(s){pred}

1-sided lower pred limit = E{Y} – tinv(%conf, Df)(s){pred}

1-sided upper pred limit = E{Y} + tinv(%conf, Df)(s){pred}

where :

Df = degrees of freedom for the error term in the model = (n-p)

s{pred} = SQRT( MSE(1+1/n + (X-Xbar)^2/SSX))

X = value at which Y is to be estimated

Xbar = average of X values

SSX = sum(Xi-Xbar)^2

Prediction Limits of Y

In Minitab, again, you can let the code do the work –

Under the “Options” button, just enter the confidence level, the X value,

and check the “Prediction Limit” box to get two-sided confidence limits.

In Excel, you will have to calculate the s{pred} value in order to calculate the

confidence limits of Y.

Confidence Limits on Coefficients

How do we find confidence limits for regression coefficients?

Again, it is similar to finding confidence limits of a sample mean

2-sided conf limits = Coeff +/- tinv(%conf, Df)(std error)

1-sided lower conf = Coeff – tinv(%conf, Df)(std error)

1-sided upper conf = Coeff + tinv(%conf, Df)(std error)

where :

Df = degrees of freedom for the error term in the model = (n-p)

Coeff and Std error comes from the regression results table

Confidence Limits for Coefficients

ANOVA

df SS MS F Significance F

Regression 1 2999.584891 2999.585 3.549601 0.10854555

Residual 6 5070.290109 845.0484

Total 7 8069.875

Coefficients Standard Error t Stat P-value Lower 95% Upper 95%

Intercept 260.278 19.35648165 13.44655 1.05E-05 212.9143234 307.6416

Mileage -0.0021 0.001116634 -1.88404 0.108546 -0.00483609 0.0006285

Excel will calculate the 2-sided confidence limits for you:

• Click the “Confidence Level” box and enter the 2-sided

confidence level value (will have to modify % if problem

is asking for one-sided confidence)

Statistics homework help

Instructions

Download the Week 1 Assignment template and complete the questions as presented. Show your work by either scanning your work and submitting it as a low-resolution graphic, typing your answers directly into the document, or copy-and-pasting your work into a Word file.

Length: No minimum required number of pages. You must provide substantial, elaborate responses answering the questions. Include examples and support your points providing evidence from scholarly articles, textbooks, and other resources used.

References: Include a minimum of 3 scholarly resources.

The completed assignment should address all of the assignment requirements, exhibit evidence of concept knowledge, and demonstrate thoughtful consideration of the content presented in the course. The writing should integrate scholarly resources, reflect academic expectations and current APA standards, and adhere to Northcentral University’s Academic Integrity Policy.

Statistics homework help

Statistical Inferences

Regression Statistical Inference

Statistical Inferences

What types of inferences can we make?

• Estimate Y given value(s) of X

• Confidence limits on estimates of Y

• Prediction limits on estimates of Y

• Confidence limits on Slope parameter

Estimates of Y

How do we find estimates of Y given X?

Expected value of Y:

E{Y} = E{B0 + B1(X) + e}

since B0, B1, and X are constants…

E{Y} = B0 + B1(X) + E{e}

E{e}=0

So E{Y} = B0 + B1(X)

Just plug the value of X into the regression equation!

Confidence Limits of Y

How do we find confidence limits for estimates of Y?

It is similar to finding confidence limits of a sample mean

2-sided conf limits = E{Y} +/- tinv(%conf, Df) (s){conf}

1-sided lower conf = E{Y} – tinv(%conf, Df) (s){conf}

1-sided upper conf = E{Y} + tinv(%conf, Df) (s){conf}

where :

Df = degrees of freedom for the error term in the model = (n-p)

s{conf} = SQRT( MSE (1/n + (X-Xbar)^2/SSX))

X = value at which Y is to be estimated

Xbar = average of X values

SSX = sum(Xi-Xbar)^2

Confidence Limits of Y

In JASP, you can let the code do the work.

In Excel, you will have to calculate the s{conf} value in order to calculate the

confidence limits of Y.

Prediction Limits of Y

How do we find prediction limits for estimates of Y?

2-sided prediction limits = E{Y} +/- tinv(%conf, Df)(s){pred}

1-sided lower pred limit = E{Y} – tinv(%conf, Df)(s){pred}

1-sided upper pred limit = E{Y} + tinv(%conf, Df)(s){pred}

where :

Df = degrees of freedom for the error term in the model = (n-p)

s{pred} = SQRT( MSE(1+1/n + (X-Xbar)^2/SSX))

X = value at which Y is to be estimated

Xbar = average of X values

SSX = sum(Xi-Xbar)^2

Prediction Limits of Y

In Minitab, again, you can let the code do the work –

Under the “Options” button, just enter the confidence level, the X value,

and check the “Prediction Limit” box to get two-sided confidence limits.

In Excel, you will have to calculate the s{pred} value in order to calculate the

confidence limits of Y.

Confidence Limits on Coefficients

How do we find confidence limits for regression coefficients?

Again, it is similar to finding confidence limits of a sample mean

2-sided conf limits = Coeff +/- tinv(%conf, Df)(std error)

1-sided lower conf = Coeff – tinv(%conf, Df)(std error)

1-sided upper conf = Coeff + tinv(%conf, Df)(std error)

where :

Df = degrees of freedom for the error term in the model = (n-p)

Coeff and Std error comes from the regression results table

Confidence Limits for Coefficients

ANOVA

df SS MS F Significance F

Regression 1 2999.584891 2999.585 3.549601 0.10854555

Residual 6 5070.290109 845.0484

Total 7 8069.875

Coefficients Standard Error t Stat P-value Lower 95% Upper 95%

Intercept 260.278 19.35648165 13.44655 1.05E-05 212.9143234 307.6416

Mileage -0.0021 0.001116634 -1.88404 0.108546 -0.00483609 0.0006285

Excel will calculate the 2-sided confidence limits for you:

• Click the “Confidence Level” box and enter the 2-sided

confidence level value (will have to modify % if problem

is asking for one-sided confidence)

Statistics homework help

Chapter 2

Study Designs

Learning Objectives (1 of 2)

List and define the components of a good study design

Compare and contrast observational and experimental study designs

Summarize the advantages and disadvantages of alternative study designs

Learning Objectives (1 of 2)

Describe the key features of a randomized controlled trial

Identify the study designs used in public health and medical studies

Study Designs

Observational studies

Case report/case series

Cross-sectional (prevalence) survey

Case-control study

Cohort study

Experimental studies

Randomized controlled (clinical) trial

Inferences

Observational studies—inferences limited to descriptions and associations; with carefully designed analysis, can make stronger inferences (statistical adjustment)

Experimental studies—cause and effect

In all studies—need careful definition of disease (outcome) and exposure (risk factor)

Which Design Is Best?

Depends on the study question

What is current knowledge on topic?

How common is disease (and risk factors)?

How long would study take; what are costs?

Ethical issues

Case Report/Case Series

Observational study

Case report—detailed report of specific features of case

Case series—systematic review of common features of a small number of cases

Advantage: cost-efficient

Disadvantages: no comparison group, no specific research question

Case Series (1 of 2)

Simplest design—description of interesting observations in a small number of individuals

Usually case series do not involve control patients (i.e., patients free of disease)

Usually lead to generation of hypotheses for more formal testing

Criticisms: not planned, no research hypotheses

Case Series (2 of 2)

Gottleib (1981) studied five young homosexual men with rare form of pneumonia and other unusual infections.

Initial report was followed by more series (26 cases in NY and CA; “cluster” in southern CA; 34 cases among Haitians, etc.)

Condition termed AIDS in 1982.

Cross-Sectional Survey (1 of 2)

Observational study conducted at a point in time

Advantages: cost-efficient, easy to implement, ethical

Disadvantages: no temporal information, non-response bias

Cross-Sectional Survey (2 of 2)

Is there an association between diabetes and cardiovascular disease (CVD)?

Patients with Diabetes

Patients without Diabetes

Patients with CVD

Prospective Cohort Study

Observational study involving a group (cohort) of individuals who meet inclusion criteria followed prospectively in time for risk factor and outcome information

Advantages: can assess temporal relationships

Disadvantages: need large numbers for rare outcomes, confounding

Cohort Study (1 of 3)

Is there an association between hypertension and cardiovascular disease?

CVD Hypertension

  No CVD

 Cohort

CVD

No Hypertension

No CVD

Study Start Time

Cohort Study (2 of 3)

Identify a group of individuals that meet inclusion criteria.

Follow prospectively in time.

Assess exposure.

Evaluate outcome status.

Cohort Study (3 of 3)

Includes persons exposed and not exposed to risk factor at outset—usually persons are disease free.

Can assess temporal relationship

Problem if disease is rare (small numbers)

Bias is less of an issue than in case-control.

Confounding may be a problem.

The Framingham Heart Study

5000+ men and women enrolled in 1948

Longitudinal cohort study

Exams every 2 years for cardiovascular risk factors—surveillance

Ancillary studies—hearing, exercise, nutrition, neurological studies

5000+ offspring and spouses enrolled in 1976

Third generation enrolled in 2002

Selection of Study Sample

Exposure group

Common risk factors—general population (e.g., Framingham Study)

Rare risk factors—special exposure cohort (e.g., soldiers exposed to agent orange)

Comparison group

Similar on all other factors that might affect outcome

Case-Control Study (1 of 3)

Observational study involving individuals with (cases) and without (controls) outcome of interest

Advantages: cost and time efficient for rare outcomes

Disadvantages: need careful selection of cases and controls, bias

Case-Control Study (2 of 3)

Is there an association between sleep position and sudden infant death syndrome (SIDS)?

Sleep prone

SIDS

Other

Sleep prone

No SIDS

Other

Study Start Time

Case-Control Study (3 of 3)

Select subjects on the basis of outcome.

Cases have disease.

Controls are free of disease.

Compare groups with respect to proportions with a history of exposure (possible cause).

Investigation is retrospective in time.

Sampling

Selection of cases

Need explicit definition to make cases as homogeneous as possible

Debate over whether cases should represent all persons with disease or specific subgroup (limit inferences)

Selection of controls

Should be comparable to cases (same exclusions)

Controls represent non-diseased persons who would have been included as cases if they had disease.

Features

Retrospective design

Cost and time efficient

Can get sufficient number of cases (useful for rare conditions)

Can investigate array of exposures

Best for diseases with long latency

Issues

Ascertainment of exposure and disease status

Both exposure and disease have occurred—hard to establish temporal relationship

Bias

Selection bias—select cases or controls and some drop out, leaving groups not comparable

Observation bias—knowledge of disease might influence reporting of exposure (over-reporting among cases)

Recall bias—retrospective (long term)

Randomized Control Trial (1 of 2)

Experimental study where patients are randomized to receive one of several comparison treatments

Advantages: gold standard from a statistical point of view, minimizes bias and confounding

Disadvantages: expensive, requires extensive monitoring, inclusion criteria can limit generalizability

Randomized Control Trial (2 of 2)

Is new drug effective in reducing hyperlipidemia (high total serum cholesterol)?

Hyperlipidemia Drug

  No Hyperlipidemia

 Sample RANDOMIZE

Hyperlipidemia

Placebo

No Hyperlipidemia

Study Start Time

Randomized Controlled Trial (Clinical Trial)

Subjects are randomized to one of two (or more) treatments, one of which may be a control treatment.

In the long run, treatment groups will be balanced in known and unknown prognostic factors.

Important that the treatments are concurrent—that the active and control treatments occur in the same period of time

Single- versus multicenter

Features

If possible, a study should be double blinded—neither the investigator nor the participant are aware of what treatment the participant is undergoing.

Sometimes it is impossible to blind the participants (for example, when the treatments being compared are medical versus surgical); but often it is possible to ensure that the people evaluating the outcome are unaware of the treatment.

Phase I: Safety

First time in humans; main objective to assess toxicity and safety in humans—pharmacokinetics

Usually involves 10 to 15 patients

Subjects are usually healthy.

Some are placebo-controlled.

Phase II: Feasibility Study

Focus still on safety

Side effects and adverse events

Efficacy is important—goal is to determine optimal dosage.

Involves a control group, and subjects are randomized.

Phase III: Clinical Trial

Focus is efficacy.

Data are collected to monitor safety.

Involves a control group (placebo, active control)

Usually involves 200 to 500 subjects

Subjects are randomized.

At least two centers

Phase IV: Post-Marketing

After approval by FDA (based on efficacy proven statistically in two or more studies, New Drug Application (NDA) reviewed within 1 year)

Focus is effectiveness.

Critical Components of RCT

Randomization

Control group—ethical issues

Monitoring

Interim analysis

Data and safety monitoring board

Data management

Reporting

Statistics homework help

PSY514

Assignment 4

Instruction:

· Use this Word document to record the calculation/analysis process and the answers.

· Submit your answers through the M7 Assignment “Quiz”

Information about the data set:

This data set is part of a data set collected by surveying a sample of young adults aged 18-20 regarding their preferences and opinions. One variable shows the social media platform used the most (SocialMedia); the other variable shows whether they support the Defund the Police movement (DefundPolice).

Perform a Chi-Square test for hypothesis testing (8 points total)

Analyze the data to answer the research question:

Do the major social media platforms vary significantly in term of user preference?

Q1. What is the null hypothesis to be tested for this research question? (1)

Q2. Which variable(s) will you be testing? (1)

Q3. Now that you’ve established how many variables you will be testing, what type of Chi-Squared test will you be running? (i.e., Chi-Squared for Goodness of Fit or Chi-Squared Test of Independence) (1)

Q4. Perform the Chi-square test to test this hypothesis. For Instagram, what is the Observed N? What is the Expected N? (1)

Q5. Report the chi-square test result in APA format, including 2 (with df and N) and p value. (2)

Q6. What is the decision of hypothesis testing (reject or fail to reject)? How do you know? (1)

Q7. What is the answer to the research question? (1)


Perform a Chi-Square test for hypothesis testing (8 points total)

Perform a chi-square test to answer the following research question:

Is support for the “Defund the Police” movement related to preferred social media platform?

(In other words, does support for the movement differ significantly across the social media platform preferences?)

Q8. What is the null hypothesis? (1)

Q9. Which variable(s) will you be testing? (1)

Q10. Now that you’ve established how many variables you will be testing, what type of Chi-Squared test will you be running? (i.e., Chi-Squared for Goodness of Fit or Chi-Squared Test of Independence) (1)

Q11. Perform the Chi-square test to test the hypothesis you just created. Report the chi-square test result in APA format, including 2 (with df and N) and p value. (2)

Q12. What is the decision of hypothesis testing (reject or fail to reject)? How do you know? (1)

Q13. What is the answer to the research question? (1)

Q14. Calculate the percentage of those who aren’t sure if they support Defund the Police movement within each social media group. Which social media group has the highest percentage? What is that percentage? (1)

Hint – (# of “not sure” people within a social media group) divided by (Total # in that social media group)


Perform a Chi-Square test for hypothesis testing (9 points total)

In another survey study on a group of 200 adults (Study B), 98 participants supported the Defund the Police movement, 96 participants opposed the Defund the Police movement, and 6 of them were unsure.

Do the adults from the data set show the same pattern as the group of adults from Study B (listed above) in terms of support for the Defund the Police movement?

Q15. What is your null hypothesis? (1)

Q16. Which variable(s) will you be testing? (1)

Q17. Now that you’ve established how many variables you will be testing, what type of Chi-Squared test will you be running? (i.e., Chi-Squared for Goodness of Fit or Chi-Squared Test of Independence) (1)

Q18. Perform the Chi-square test to test the hypothesis you just created. For people who support the movement, what is the Observed N? What about Expected N? (2)

Q19. Report the chi-square test result in APA format, including 2 (with df and N) and p value. (1)

Q20. What is the decision of hypothesis testing (reject or fail to reject)? How do you know? (1)

Q21. What is the answer to the research question? (1)

Q22. Comparing our data with the other study, the difference in the number of supporters is the largest for which opinion (support, oppose, or unsure) about the Defund the Police movement? (1)


And finally…

Q23. Thank you again for your flexibility this session as we created new materials for this course specifically designed for Forensic Psychology students! Because you were all so patient, we wanted to throw you some freebie points for this assignment by giving us some feedback. On the quiz, there will be an open-ended question for you to let us know how we can improve the course. Note that, to get points for this question, you need to both (a) provide feedback and (b) check a box indicating that you provided feedback. Thank you in advance for your thoughtful responses! (5)

Statistics homework help

Please cite as: Rivera, J. (2015). Semester Research Project in Applied Business Statistics.
Carthage College.

21 APRIL 2016, 12:36:00 PM

S t a t i s t i c s S e m e s t e r P r o j e c t R u b r i c

The rubric reflects the student learning outcomes for the course that are listed in the syllabus and
here:

C o u r s e S t u d e n t L e a r n i n g O u t c o m e s

1. Students will determine descriptive measures of central tendency and dispersion for data
sets and explain what they mean.

2. Students will demonstrate understanding of the concept of probability by defining and
explaining what a p-value is and what it means when applied to a statistical test of
significance.

3. Students will set up and execute statistical tests for differences, similarities, correlations,
and the general linear model and explain what they mean (parametric and non-parametric).

4. Students will determine whether their data set requires a parametric or non-parametric
statistical test.

5. Students will explain the concepts of estimation and confidence intervals and use them to
determine whether the sample size of their data sets is adequate to measure a statistical
outcome.

6. Students will apply sampling techniques through the extraction of data subset from a large
database for analysis.

7. Students will use data visualization techniques to explain their findings.
8. Students will demonstrate mastery of the hardware and software required to complete the

course.

R u b r i c f o r F i n a l S e m e s t e r P r o j e c t

The final project which consists of the paper, poster, and presentation will be evaluated on the
following rubric:

A r e a Superior

4
Very Good
3

Adequate
2

Baseline
1

T o p i c s e l e c t i o n The student
Identifies a
creative, focused,
and manageable
topic that
addresses
potentially
significant yet
previously less-
explored aspects
of the topic.

The student
Identifies a
focused and
manageable/
doable topic
that
appropriately
addresses
relevant
aspects of the
topic.

The student
Identifies a topic
that while
manageable/
doable, is too
narrowly
focused and
leaves out
relevant aspects
of the topic.

The student
Identifies a topic
that is far too
general and wide-
ranging as to be
manageable and
doable.

21 APRIL 2016, 12:36:00 PM 2

A r e a Superior
4

Very Good
3

Adequate
2

Baseline
1

H y p o t h e s i s
D e f i n i t i o n

The student
Proposes
hypotheses that
indicates a deep
comprehension of
the problem.
Hypotheses are
sensitive to
contextual factors
as well as all of the
following: ethical,
logical, and
cultural
dimensions of the
problem.

The student
Proposes one
or more
hypotheses
that indicates
comprehension
of the problem.
Hypotheses are
sensitive to
contextual
factors as well
as the one of
the following:
ethical, logical,
or cultural
dimensions of
the problem.

The student
Proposes one
hypothesis that
is formulaic or
generic rather
than individually
designed to
address the
specific
contextual
factors of the
problem.

The student
Proposes a
hypothesis that is
difficult to
evaluate because
it is vague or only
indirectly
addresses the
problem
statement.

D e s c r i p t i v e
S t a t i s t i c s

Student will use an
appropriate range
of descriptive
statistics is listed
with sound and
deeper explanation
about their
meaning.

Students will
use an
appropriate
range of
descriptive
statistics along
with an with
adequate
explanation
about their
meaning.

Student will use
an appropriate
range of
descriptive
statistics is
listed.

Student will use
some descriptive
statistics

D a t a
V i s u a l i z a t i o n

Student creates a
set of graphs and
charts that explain
the data more
clearly. The
visualizations
explain the “story
of the data.” The
graphs and
visualizations are
also elegantly
designed.

Student is able
to create a set
of graphs and
charts that
explain the
data clearly.
The
visualizations
also explain the
“story of the
data.”

Student is able
to create a set
of graphs and
charts that
somewhat
explain the data.

Student is able to
create a graph or
chart of the data.

21 APRIL 2016, 12:36:00 PM 3

A r e a Superior
4

Very Good
3

Adequate
2

Baseline
1

I n f e r e n t i a l
S t a t i s t i c a l
T e s t s S e l e c t e d

Student selects
appropriate
statistical tests
and forms a
methodology that
is skillfully
developed and
executed.
Appropriate
methodology or
theoretical
frameworks may
be synthesized
from across
disciplines or from
relevant sub
disciplines.
Calculations
attempted are
essentially all
successful and
sufficiently
comprehensive to
solve the problem.
Calculations are
also presented
elegantly (clearly,
concisely, etc.)

Student
successfully
selects and
executes
statistical tests
and the
methodology or
theoretical
framework is
appropriately
developed;
however, more
subtle
elements are
ignored or
unaccounted
for.
Calculations
attempted are
essentially all
successful and
sufficiently
comprehensive
to solve the
problem.

Student selects
an appropriate
statistical test
but the
methodology or
theoretical
framework are
missing,
incorrectly
developed, or
unfocused.
Calculations
attempted are
either
unsuccessful or
represent only a
portion of the
calculations
required to
comprehensively
solve the
problem.

Student selects
tests that are
inappropriate for
the problem in
question. Design
demonstrates a
misunderstanding
of the theoretical
framework.
Calculations
attempted are
unsuccessful and
not
comprehensive

21 APRIL 2016, 12:36:00 PM 4

A r e a Superior
4

Very Good
3

Adequate
2

Baseline
1

A n a l y s i s o f
I n f e r e n t i a l
S t a t i s t i c s

Student is able to
report the test
statistic results
and relate them to
the hypotheses.
Student continues
to explain the
meaning of the
results along with
the larger context
of the problem.
Uses the
quantitative
analysis of data as
the basis for deep
and thoughtful
judgments,
drawing insightful,
carefully qualified
conclusions from
this work

Student is able
to report the
test statistic
results and
relate them to
the hypotheses.
Student is able
to explain the
results.
Uses the
quantitative
analysis of data
as the basis for
competent
judgments,
drawing
reasonable and
appropriately
qualified
conclusions
from this work.

Student is able
to report the test
statistic results
and relate them
to the
hypotheses.
Uses the
quantitative
analysis of data
as the basis for
judgement
(without
inspiration,
nuance, or
ordinary drawing
plausible
conclusions
from this work.

Student is able to
report the test
statistic results
Uses the
quantitative
analysis of data
as the basis for
tentative, basic
judgments,
although is
hesitant or
uncertain about
drawing
conclusions from
this work.

21 APRIL 2016, 12:36:00 PM 5

A r e a Superior
4

Very Good
3

Adequate
2

Baseline
1

C o n c l u s i o n s
a n d
C o m m u n i c a t i o n

Student states a
conclusion focused
solely on the
inquiry findings.
The conclusion
arises specifically
from and responds
specifically to the
inquiry findings.
The student uses
quantitative
information in
connection with
the argument or
purpose of the
work, though data
may be presented
in a less than
completely
effective format or
some parts of the
explication may be
uneven.
The student
insightfully
discusses in detail
relevant ideas and
supported
limitations and
implications.

Student states
a conclusion
focused solely
on the inquiry
findings. The
conclusion
arises
specifically
from and
responds
specifically to
the inquiry
findings.
The student
uses
quantitative
information in
connection
with the
argument or
purpose of the
work, though
data may be
presented in a
less than
completely
effective
format or some
parts of the
explication may
be uneven.
Student
discusses
relevant and
supported
limitations and
implications.

Student states a
general
conclusion that,
because it is so
general, also
applies beyond
the scope of the
inquiry findings.
Student uses
quantitative
information, but
does not
effectively
connect it to the
argument or
purpose of the
work. The
student presents
relevant and
supported
limitations and
implications.

Student states an
ambiguous,
illogical, or
unsupportable
conclusion from
inquiry findings.
Presents an
argument for
which
quantitative
evidence is
pertinent, but
does not provide
adequate explicit
numerical
support. (May use
quasi-quantitative
words such as
“many,” “few,”
“increasing,”
“small,” and the
like in place of
actual quantities.)
The student
presents
limitations and
implications, but
they are possibly
irrelevant and
unsupported.

Rubric adapted from Liberal Education & America’s Promise Value Rubrics, Association of
American Colleges and Universities, 2010

Statistics homework help

1

Math 140 Exam 2
COC Spring 2022

150 Points

Question 1 (30 points)
Match the following vocabulary words in the table below with the corresponding definitions.

Confidence Interval Hypothesis Test Standard Error Alternative Hypothesis

Randomized Simulation Random Sample Random Assignment Random Chance

Population Sampling Variability Significance Level Type II Error

One-Population Mean
T-Test Statistic

Quantitative Data One-Population
Proportion Z-Test

Statistic

Categorical Data

Critical Value Statistic Parameter Census

Type I Error Bootstrap Distribution Margin of Error Beta Level

Bootstrapping Null Hypothesis P-value Point Estimate

a. A number we compare our test statistic to in order to determine significance. In a sampling

distribution or a theoretical distribution approximating the sampling distribution, the critical

value shows us where the tail or tails are. The test statistic must fall in the tail to be significant.

b. Also called the Alpha Level. If the P-value is lower than this number, then the sample data

significantly disagrees with the null hypothesis and is unlikely to have happened by random

chance. This is also the probability of making a type 1 error.

c. A statement about the population that does not involve equality. It is often a statement about a

“significant difference”, “significant change”, “relationship” or “effect”.

d. The collection of all people or objects you want to study.

e. A number calculated from sample data in order to understand the characteristics of the data.

f. When biased sample data leads you to support the alternative hypothesis when the alternative

hypothesis is actually wrong in the population.

g. Another word for sampling variability. The principle that random samples from the same

population will usually be different and give very different statistics.

h. Data in the form of numbers that measure or count something. They usually have units and

taking an average makes sense.

i. Taking many random samples values from one original real random sample with replacement.

j. Collecting data from everyone in a population.

2

k. Collecting data from a population in such a way that every person in the population has an

approximately equal chance of being chosen. This technique tends to give us data with less

sampling bias.

l. The probability of getting the sample data or more extreme because of sampling variability (by

random chance) if the null hypothesis is true.

m. The sample proportion is this many standard errors above or below the population proportion in

the null hypothesis.

n. Take a group of people or objects and randomly put them into two or more groups. This is a

technique used in experiments to create similar groups. Similar groups help to control

confounding variables so that the scientist can prove cause and effect.

o. Data in the form of labels that tell us something about the people or objects in the data set.

p. The standard deviation of a sampling distribution. The distance that typical sample statistics are

from the center of the sampling distribution. Since the center of the sampling distributions is

usually close to the population parameter, the standard error tells us how far typical sample

statistics are from the population parameter.

q. When someone takes a sample statistic and then claims that it is the population parameter.

r. Two numbers that we think a population parameter is in between. Can be calculated by either a

bootstrap distribution or by adding and subtracting the sample statistic and the margin of error.

s. When biased sample data leads you fail to reject the null hypothesis when the null hypothesis is

actually wrong in the population.

t. The sample mean is this many standard errors above or below the population mean in the null

hypothesis.

u. Putting many bootstrap statistics on the same graph in order to simulate the sampling variability

in a population, calculate standard error, and create a confidence interval. The center of the

bootstrap distribution is the original real sample statistic.

v. The probability of making a type 2 error.

w. A statement about the population that involves equality. It is often a statement about “no

change”, “no relationship” or “no effect”.

x. Random samples values and sample statistics are usually different from each other and usually

different from the population parameter.

y. Total distance that a sample statistic might be from the population parameter. For normal

sampling distributions and a 95% confidence interval, the margin of error is approximately twice

as large as the standard error.

z. A number that describes the characteristics of a population like a population mean or a

population percentage. Can be calculated from an unbiased census, but is often just a guess

about the population.

aa. A procedure for testing a claim about a population.

bb. A technique for visualizing sampling variability in a hypothesis test. The computer assumes the

null hypothesis is true, and then generates random samples. If the sample data or test statistic

falls in the tail, then the sample data significantly disagrees with the null hypothesis. This

technique can also calculate the P-value without a formula.

3

Question 2 (25 Points)
2-Population Mean Hypothesis Test

a. Determine if the following two-population mean tests are matched pair or independent groups.

b. Write the null and alternative hypothesis. Include the claim and what type of test.

c. Check all of the assumptions for a two-population mean T-test. Explain your answers. Does the

problem meets all the assumptions?

d. Write a sentence to explain the T-test statistic.

e. Use the test statistic and the critical value to determine if the sample data significantly disagrees

with the null hypothesis. Explain your answer

f. Write a sentence to explain the P-value.

g. Use the P-value and significance level to determine if the sample data could have occurred by

random chance (sampling variability) or is it unlikely to random chance? Explain your answer.

h. Should we reject the null hypothesis or fail to reject the null hypothesis? Explain your answer.

i. Write a conclusion for the hypothesis test. Explain your conclusion in plain language.

j. Is the categorical variable related to the quantitative variable? Explain your answer.

Here is the scenario.

Researchers collected data on traffic flow, number of shoppers, and traffic accident-related emergency

room admissions on Friday the 13th and the previous Friday, Friday the 6th. They randomly selected 40

Friday the 13ths and 40 Friday the 6ths over a ten-year period. Also given are some sample statistics,

where the difference is the number of cars on the 6th minus the number of cars on the 13th. We claim

that the difference is not zero. (Use a 5% significance level).

Friday 6th Friday 13th Difference

�̅� 128,385 126,550 1835

𝑠 7,664 7,259 405

𝑛 40 40 40

The T-test statistic is ±4.94 and critical value is 2.38. The p-value is < 0.01.

Question 3 (15 Points)
2-Population Mean Confidence Interval

a. Does the data meet the assumptions for inference with two population proportions or two

population means? If it is two means, are the groups independent or matched pair? List the

assumptions needed and how the problem meets them or does not meet them.

b. Does the confidence interval indicate that the mean from population 1 is higher, lower, or not

significantly different from population 2? Explain how you know.

c. Write the two-population confidence interval sentence explaining this confidence interval.

The scenario is the same as in question 2. Also included here is the confidence interval (1518, 2151)

with confidence level 95%.

4

Question 4 (20 Points)
1-Population Proportion Hypothesis Test

a. Give the null and alternative hypothesis. Which is the claim? Is this a right-tailed, left-tailed, or

two-tailed test? Explain how you know what tail to use.

b. Check the assumptions.

c. Give the test statistic and write the standard sentence to explain it. Compare your test statistic

to the critical value. Did the sample data significantly disagree with the null hypothesis? Explain

how.

d. Give the p-value and write the definition sentence to explain it. Could the sample data have

happened because of sampling variability (random chance) or is it unlikely to be sampling

variability? Explain why.

e. Compare the p-value to the significance level. State whether you reject the null hypothesis or

fail to reject the null hypothesis. Explain your answer.

f. Write the standard conclusion.

g. Explain your conclusion in easy to understand language.

Here is the scenario.

An online source suggests that one out of every three people in the U.S have high blood pressure and

the population proportion of U.S. adults is 33.3%. Another website disagrees with this and claims that

the true percentage of U.S. adults with high blood pressure is dramatically lower than 1 in 3 (33.3%). A

random sample of 500 U.S. adults found that 165 of them had high blood pressure. Use the printout and

a 10% significance level to test the claim that less than 33% of U.S. adults have high blood pressure.

N Sample
Proportion

Significance
Level

Critical Value Test Statistic Z P-value

500 0.33 0.10 -1.282 -0.142 0.4434

Question 5 (10 Points)
1-Population Proportion Bootstrap Confidence Interval

a. Does the data meet the assumptions for a bootstrap confidence interval? Explain your answer.

b. How many bootstrap samples were taken (see picture below)?

c. What is the shape of the bootstrap distribution?

d. Write the upper and lower limits of the bootstrap confidence interval.

e. Write a sentence to explain the bootstrap confidence interval estimate of the population

proportion.

Here is the scenario.

An experiment employing randomization was conducted to see what percentage of rats would show

empathy toward fellow rats in distress. Of the 30 total rats in the study, 23 showed empathy. Use the

bootstrap distribution to find a 99% confidence interval for the population proportion.

5

Question 6 (20 Points)
a. State the Central Limit Theorem for Means and explain the ideas behind it.

b. Describe the process of making a sampling distribution.

c. What is a point estimate? Discuss how point estimates create confusion for people reading

articles and scientific reports.

d. What conditions should be met to ensure that a sampling distribution of sample proportions is

normal?

Question 7 (5 Points)
State the assumptions for a one-population variance or standard deviation confidence interval.

6

Question 8 (5 Points)
Use the following formulas to identify the sample statistic (p-hat or x-bar or s) and the margin of error.

𝑆𝑎𝑚𝑝𝑙𝑒 𝑆𝑡𝑎𝑡𝑖𝑠𝑡𝑖𝑐 =
(𝑈𝑝𝑝𝑒𝑟 𝐿𝑖𝑚𝑖𝑡 + 𝐿𝑜𝑤𝑒𝑟 𝐿𝑖𝑚𝑖𝑡)

2

𝑀𝑎𝑟𝑔𝑖𝑛 𝑜𝑓 𝐸𝑟𝑟𝑜𝑟 =
(𝑈𝑝𝑝𝑒𝑟 𝐿𝑖𝑚𝑖𝑡 − 𝐿𝑜𝑤𝑒𝑟 𝐿𝑖𝑚𝑖𝑡)

2

A 95% confidence interval estimate of the population proportion of pies in a county fair in Ohio is

(0.46, 0.52).

Question 9 (20 Points)
Type I and II Errors

Scenario I:
Mike and his advertisement team have created an advertisement plan for a new flavor of soda. Right

now, approximately 16% of soda drinkers are purchasing this flavor. Mike needs to show his bosses that

his advertisement plan will increase the percentage of soda drinkers purchasing this new flavor. If Mike’s

advertising team succeeds in increasing the percentage of customers that prefer this new flavor, then

the company will increase supply and make more of the soda to meet demand. If not, then the company

will keep the supply as it currently is. After the advertising changes, Mike takes a random sample of

customers to determine if the percentage of soda drinkers that like the new flavor has increased. (They

are currently using a 5% significance level).

𝐻0: 𝜋 = 0.16 (𝑇ℎ𝑒 𝑐𝑜𝑚𝑝𝑎𝑛𝑦 𝑤𝑖𝑙𝑙 𝑛𝑜𝑡 𝑖𝑛𝑐𝑟𝑒𝑎𝑠𝑒 𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝑜𝑓 𝑡ℎ𝑒 𝑛𝑒𝑤 𝑓𝑙𝑎𝑣𝑜𝑟 𝑜𝑓 𝑠𝑜𝑑𝑎. )

𝐻𝐴: 𝜋 > 0.16 (𝑇ℎ𝑒 𝑐𝑜𝑚𝑝𝑎𝑛𝑦 𝑤𝑖𝑙𝑙 𝑖𝑛𝑐𝑟𝑒𝑎𝑠𝑒 𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝑜𝑓 𝑡ℎ𝑒 𝑛𝑒𝑤 𝑓𝑙𝑎𝑣𝑜𝑟 𝑜𝑓 𝑠𝑜𝑑𝑎. )

a. Write a description of a type 1 error and the possible consequences of that error in the context

of the problem.

b. Write a description of a type 2 error and possible consequences of that error in the context of

the problem.

c. Would you recommend any changes to the significance level or sample size based on what you

know about the type 1 and type 2 errors in this problem? Explain.

Scenario II:
A global sportswear company is contemplating contributing money to a political candidate in the next

election. The managers of the company do not want to contribute unless they are sure the candidate

will get the majority of the population vote and win the election. Otherwise, the company will not

contribute to the candidates’ campaign. (They are currently using a 10% significance level).

𝐻0: 𝜋 ≤ 0.5 (𝑇ℎ𝑒 𝑐𝑜𝑚𝑝𝑎𝑛𝑦 𝑤𝑖𝑙𝑙 𝑛𝑜𝑡 𝑐𝑜𝑛𝑡𝑟𝑖𝑏𝑢𝑡𝑒 𝑡𝑜 𝑡ℎ𝑒 𝑝𝑜𝑙𝑖𝑡𝑖𝑐𝑎𝑙 𝑐𝑎𝑛𝑑𝑖𝑑𝑎𝑡𝑒𝑠
′ 𝑐𝑎𝑚𝑝𝑎𝑖𝑔𝑛. )

𝐻𝐴: 𝜋 > 0.5 (𝑇ℎ𝑒 𝑐𝑜𝑚𝑝𝑎𝑛𝑦 𝑤𝑖𝑙𝑙 𝑐𝑜𝑛𝑡𝑟𝑖𝑏𝑢𝑡𝑒 𝑡𝑜 𝑡ℎ𝑒 𝑝𝑜𝑙𝑖𝑡𝑖𝑐𝑎𝑙 𝑐𝑎𝑛𝑑𝑖𝑑𝑎𝑡𝑒𝑠
′ 𝑐𝑎𝑚𝑝𝑎𝑖𝑔𝑛. )

7

a. Write a description of a type 1 error and the possible consequences of that error in the context

of the problem.

b. Write a description of a type 2 error and possible consequences of that error in the context of

the problem.

c. Would you recommend any changes to the significance level or sample size based on what you

know about the type 1 and type 2 errors in this problem? Explain.

Statistics homework help

Instructions

Download the Week 1 Assignment template and complete the questions as presented. Show your work by either scanning your work and submitting it as a low-resolution graphic, typing your answers directly into the document, or copy-and-pasting your work into a Word file.

Length: No minimum required number of pages. You must provide substantial, elaborate responses answering the questions. Include examples and support your points providing evidence from scholarly articles, textbooks, and other resources used.

References: Include a minimum of 3 scholarly resources.

The completed assignment should address all of the assignment requirements, exhibit evidence of concept knowledge, and demonstrate thoughtful consideration of the content presented in the course. The writing should integrate scholarly resources, reflect academic expectations and current APA standards, and adhere to Northcentral University’s Academic Integrity Policy.

Statistics homework help

Week One Journal

Course Reflection

Provide reflection of this week that contains 1 paragraph, which address at least one or two of the following topics:

Use the chapter power points to answer the topics below.

· Learning (i.e., information learned from course and/or content)

· Likes (i.e., liked most about the course and/or content)

· Dislikes (i.e., liked least about the course and/or content)

· Suggestions (i.e., suggestions for improvement about the course, content and/or assignments)

Statistics homework help

PSY514

Assignment 4

Instruction:

· Use this Word document to record the calculation/analysis process and the answers.

· Submit your answers through the M7 Assignment “Quiz”

Information about the data set:

This data set is part of a data set collected by surveying a sample of young adults aged 18-20 regarding their preferences and opinions. One variable shows the social media platform used the most (SocialMedia); the other variable shows whether they support the Defund the Police movement (DefundPolice).

Perform a Chi-Square test for hypothesis testing (8 points total)

Analyze the data to answer the research question:

Do the major social media platforms vary significantly in term of user preference?

Q1. What is the null hypothesis to be tested for this research question? (1)

Q2. Which variable(s) will you be testing? (1)

Q3. Now that you’ve established how many variables you will be testing, what type of Chi-Squared test will you be running? (i.e., Chi-Squared for Goodness of Fit or Chi-Squared Test of Independence) (1)

Q4. Perform the Chi-square test to test this hypothesis. For Instagram, what is the Observed N? What is the Expected N? (1)

Q5. Report the chi-square test result in APA format, including 2 (with df and N) and p value. (2)

Q6. What is the decision of hypothesis testing (reject or fail to reject)? How do you know? (1)

Q7. What is the answer to the research question? (1)


Perform a Chi-Square test for hypothesis testing (8 points total)

Perform a chi-square test to answer the following research question:

Is support for the “Defund the Police” movement related to preferred social media platform?

(In other words, does support for the movement differ significantly across the social media platform preferences?)

Q8. What is the null hypothesis? (1)

Q9. Which variable(s) will you be testing? (1)

Q10. Now that you’ve established how many variables you will be testing, what type of Chi-Squared test will you be running? (i.e., Chi-Squared for Goodness of Fit or Chi-Squared Test of Independence) (1)

Q11. Perform the Chi-square test to test the hypothesis you just created. Report the chi-square test result in APA format, including 2 (with df and N) and p value. (2)

Q12. What is the decision of hypothesis testing (reject or fail to reject)? How do you know? (1)

Q13. What is the answer to the research question? (1)

Q14. Calculate the percentage of those who aren’t sure if they support Defund the Police movement within each social media group. Which social media group has the highest percentage? What is that percentage? (1)

Hint – (# of “not sure” people within a social media group) divided by (Total # in that social media group)


Perform a Chi-Square test for hypothesis testing (9 points total)

In another survey study on a group of 200 adults (Study B), 98 participants supported the Defund the Police movement, 96 participants opposed the Defund the Police movement, and 6 of them were unsure.

Do the adults from the data set show the same pattern as the group of adults from Study B (listed above) in terms of support for the Defund the Police movement?

Q15. What is your null hypothesis? (1)

Q16. Which variable(s) will you be testing? (1)

Q17. Now that you’ve established how many variables you will be testing, what type of Chi-Squared test will you be running? (i.e., Chi-Squared for Goodness of Fit or Chi-Squared Test of Independence) (1)

Q18. Perform the Chi-square test to test the hypothesis you just created. For people who support the movement, what is the Observed N? What about Expected N? (2)

Q19. Report the chi-square test result in APA format, including 2 (with df and N) and p value. (1)

Q20. What is the decision of hypothesis testing (reject or fail to reject)? How do you know? (1)

Q21. What is the answer to the research question? (1)

Q22. Comparing our data with the other study, the difference in the number of supporters is the largest for which opinion (support, oppose, or unsure) about the Defund the Police movement? (1)


And finally…

Q23. Thank you again for your flexibility this session as we created new materials for this course specifically designed for Forensic Psychology students! Because you were all so patient, we wanted to throw you some freebie points for this assignment by giving us some feedback. On the quiz, there will be an open-ended question for you to let us know how we can improve the course. Note that, to get points for this question, you need to both (a) provide feedback and (b) check a box indicating that you provided feedback. Thank you in advance for your thoughtful responses! (5)

Statistics homework help

AME 500B
Final Exam
(3 Hours)

5/10/20

Before beginning any problem, read the entire exam. Do the problem
that seems simplest first. Please begin each problem on a separate
page of your own paper. Open book and notes, but no internet. Submit
to Final Submission Box

(20) 1. Consider the following wave equation for an infinite string:

( )
2 2

2
2 2 , 0c u x tt x

 ∂ ∂
− = ∂ ∂ 

.

Using the coordinate transformation
,x ct x ctξ η≡ + ≡ −

show that
( ) ( )( )2 , , ,

0
u x tξ η ξ η

ξ η

=
∂ ∂

.

(15) 2. If ( ) ( ), 0u x f x= and
( ) ( )

0

,

t

u x t
g x

t
=


=


, show the solution to the wave

equation of Problem 1 is

( ) ( ) ( ) ( )1 1,
2 2

x ct

x ct
u x t f x ct f x ct dt g t

c

+

′ ′= + + − +   ∫ .

(20) 3. Solve the wave equation

( )
2 2

2
2 2 , 0c u x tt x

 ∂ ∂
− = ∂ ∂ 

subject to the boundary conditions
( ) ( )0, , 0u t u L t= =

and initial conditions

( ) ( ) ( ) ( )
0

, 0
, 0 ,

t

u x
u x f x g x

t
=


= =

to show that the solution satisfies
( ) ( ) ( ), vu x t x ct w x ct= + + − .

(10) 4. Is the polynomial
2 2( , ) 2P x y x y ixy= + −

analytic? What two changes will make this polynomial analytic?

(15) 5. If f(z) is an analytic function, show that

( ) ( ) ( )
22

2
f z f z f z

x y

  ∂ ∂   ′+ =   ∂ ∂     
.

Hint: ( ) vuf z i
x x
∂ ∂

′ = +
∂ ∂

(10) 6. Criticize the following argument: Since

1

0

1

1 ;
1

k

k

k

k

z
z

z
z

z
z

=


=

=

= +

therefore

0
1 1

z z
z z
+ =

− −
.

(20) 7. Evaluate the following integral for k < 1:

( )
2

0

1
1 cos

I d
k

π

θ
θ

=
+  

∫ .

(20) 8. Consider the following Sturm-Liouville problem:

( ) ( )2 0, 0 1
d xd

x k x
dx dx

β φ φ β
 

+ = < < 
 

.

satisfying homogeneous BC. State at least 7 features of the solution that are known
without having to solve the equation.

(25) 9.a. Directly from the solution of the following 2-D heat transfer equation:

( )
2 2

2 2 , , 0, 0 , 0u x y t x a y bt x y
 ∂ ∂ ∂

− − = < < < < ∂ ∂ ∂ 

with homogeneous BC
( ) ( )
( ) ( )
0, , , , 0

, 0, , , 0

u y t u a y t

u x t u x b t

= =

= =

and IC
( ) ( ) ( ), , 0u x y f x g y= ,

show that
( ) ( ) ( )1 2, , , ,u x y t u x t u y t= ,

where

( )

( ) ( )
( ) ( )

( )

( ) ( )
( ) ( )

2

12

1 1

1

2

22

2 2

2

, 0, 0 ;

0, 0, , 0

, 0

, 0, 0

0, 0, , 0

, 0 .

u x t x a
t x

u t u a t

u x f x

u y t y b
t y

u t u b t

u y g y

 ∂ ∂
− = < < ∂ ∂ 

= =

=

 ∂ ∂
− = < < ∂ ∂ 

= =

=

b. Predict what the solution will be for 3D with the same BC in the third

dimension and a corresponding product IC.

Statistics homework help

1

Math 140 Exam 2
COC Spring 2022

150 Points

Question 1 (30 points)
Match the following vocabulary words in the table below with the corresponding definitions.

Confidence Interval Hypothesis Test Standard Error Alternative Hypothesis

Randomized Simulation Random Sample Random Assignment Random Chance

Population Sampling Variability Significance Level Type II Error

One-Population Mean
T-Test Statistic

Quantitative Data One-Population
Proportion Z-Test

Statistic

Categorical Data

Critical Value Statistic Parameter Census

Type I Error Bootstrap Distribution Margin of Error Beta Level

Bootstrapping Null Hypothesis P-value Point Estimate

a. A number we compare our test statistic to in order to determine significance. In a sampling

distribution or a theoretical distribution approximating the sampling distribution, the critical

value shows us where the tail or tails are. The test statistic must fall in the tail to be significant.

b. Also called the Alpha Level. If the P-value is lower than this number, then the sample data

significantly disagrees with the null hypothesis and is unlikely to have happened by random

chance. This is also the probability of making a type 1 error.

c. A statement about the population that does not involve equality. It is often a statement about a

“significant difference”, “significant change”, “relationship” or “effect”.

d. The collection of all people or objects you want to study.

e. A number calculated from sample data in order to understand the characteristics of the data.

f. When biased sample data leads you to support the alternative hypothesis when the alternative

hypothesis is actually wrong in the population.

g. Another word for sampling variability. The principle that random samples from the same

population will usually be different and give very different statistics.

h. Data in the form of numbers that measure or count something. They usually have units and

taking an average makes sense.

i. Taking many random samples values from one original real random sample with replacement.

j. Collecting data from everyone in a population.

2

k. Collecting data from a population in such a way that every person in the population has an

approximately equal chance of being chosen. This technique tends to give us data with less

sampling bias.

l. The probability of getting the sample data or more extreme because of sampling variability (by

random chance) if the null hypothesis is true.

m. The sample proportion is this many standard errors above or below the population proportion in

the null hypothesis.

n. Take a group of people or objects and randomly put them into two or more groups. This is a

technique used in experiments to create similar groups. Similar groups help to control

confounding variables so that the scientist can prove cause and effect.

o. Data in the form of labels that tell us something about the people or objects in the data set.

p. The standard deviation of a sampling distribution. The distance that typical sample statistics are

from the center of the sampling distribution. Since the center of the sampling distributions is

usually close to the population parameter, the standard error tells us how far typical sample

statistics are from the population parameter.

q. When someone takes a sample statistic and then claims that it is the population parameter.

r. Two numbers that we think a population parameter is in between. Can be calculated by either a

bootstrap distribution or by adding and subtracting the sample statistic and the margin of error.

s. When biased sample data leads you fail to reject the null hypothesis when the null hypothesis is

actually wrong in the population.

t. The sample mean is this many standard errors above or below the population mean in the null

hypothesis.

u. Putting many bootstrap statistics on the same graph in order to simulate the sampling variability

in a population, calculate standard error, and create a confidence interval. The center of the

bootstrap distribution is the original real sample statistic.

v. The probability of making a type 2 error.

w. A statement about the population that involves equality. It is often a statement about “no

change”, “no relationship” or “no effect”.

x. Random samples values and sample statistics are usually different from each other and usually

different from the population parameter.

y. Total distance that a sample statistic might be from the population parameter. For normal

sampling distributions and a 95% confidence interval, the margin of error is approximately twice

as large as the standard error.

z. A number that describes the characteristics of a population like a population mean or a

population percentage. Can be calculated from an unbiased census, but is often just a guess

about the population.

aa. A procedure for testing a claim about a population.

bb. A technique for visualizing sampling variability in a hypothesis test. The computer assumes the

null hypothesis is true, and then generates random samples. If the sample data or test statistic

falls in the tail, then the sample data significantly disagrees with the null hypothesis. This

technique can also calculate the P-value without a formula.

3

Question 2 (25 Points)
2-Population Mean Hypothesis Test

a. Determine if the following two-population mean tests are matched pair or independent groups.

b. Write the null and alternative hypothesis. Include the claim and what type of test.

c. Check all of the assumptions for a two-population mean T-test. Explain your answers. Does the

problem meets all the assumptions?

d. Write a sentence to explain the T-test statistic.

e. Use the test statistic and the critical value to determine if the sample data significantly disagrees

with the null hypothesis. Explain your answer

f. Write a sentence to explain the P-value.

g. Use the P-value and significance level to determine if the sample data could have occurred by

random chance (sampling variability) or is it unlikely to random chance? Explain your answer.

h. Should we reject the null hypothesis or fail to reject the null hypothesis? Explain your answer.

i. Write a conclusion for the hypothesis test. Explain your conclusion in plain language.

j. Is the categorical variable related to the quantitative variable? Explain your answer.

Here is the scenario.

Researchers collected data on traffic flow, number of shoppers, and traffic accident-related emergency

room admissions on Friday the 13th and the previous Friday, Friday the 6th. They randomly selected 40

Friday the 13ths and 40 Friday the 6ths over a ten-year period. Also given are some sample statistics,

where the difference is the number of cars on the 6th minus the number of cars on the 13th. We claim

that the difference is not zero. (Use a 5% significance level).

Friday 6th Friday 13th Difference

�̅� 128,385 126,550 1835

𝑠 7,664 7,259 405

𝑛 40 40 40

The T-test statistic is ±4.94 and critical value is 2.38. The p-value is < 0.01.

Question 3 (15 Points)
2-Population Mean Confidence Interval

a. Does the data meet the assumptions for inference with two population proportions or two

population means? If it is two means, are the groups independent or matched pair? List the

assumptions needed and how the problem meets them or does not meet them.

b. Does the confidence interval indicate that the mean from population 1 is higher, lower, or not

significantly different from population 2? Explain how you know.

c. Write the two-population confidence interval sentence explaining this confidence interval.

The scenario is the same as in question 2. Also included here is the confidence interval (1518, 2151)

with confidence level 95%.

4

Question 4 (20 Points)
1-Population Proportion Hypothesis Test

a. Give the null and alternative hypothesis. Which is the claim? Is this a right-tailed, left-tailed, or

two-tailed test? Explain how you know what tail to use.

b. Check the assumptions.

c. Give the test statistic and write the standard sentence to explain it. Compare your test statistic

to the critical value. Did the sample data significantly disagree with the null hypothesis? Explain

how.

d. Give the p-value and write the definition sentence to explain it. Could the sample data have

happened because of sampling variability (random chance) or is it unlikely to be sampling

variability? Explain why.

e. Compare the p-value to the significance level. State whether you reject the null hypothesis or

fail to reject the null hypothesis. Explain your answer.

f. Write the standard conclusion.

g. Explain your conclusion in easy to understand language.

Here is the scenario.

An online source suggests that one out of every three people in the U.S have high blood pressure and

the population proportion of U.S. adults is 33.3%. Another website disagrees with this and claims that

the true percentage of U.S. adults with high blood pressure is dramatically lower than 1 in 3 (33.3%). A

random sample of 500 U.S. adults found that 165 of them had high blood pressure. Use the printout and

a 10% significance level to test the claim that less than 33% of U.S. adults have high blood pressure.

N Sample
Proportion

Significance
Level

Critical Value Test Statistic Z P-value

500 0.33 0.10 -1.282 -0.142 0.4434

Question 5 (10 Points)
1-Population Proportion Bootstrap Confidence Interval

a. Does the data meet the assumptions for a bootstrap confidence interval? Explain your answer.

b. How many bootstrap samples were taken (see picture below)?

c. What is the shape of the bootstrap distribution?

d. Write the upper and lower limits of the bootstrap confidence interval.

e. Write a sentence to explain the bootstrap confidence interval estimate of the population

proportion.

Here is the scenario.

An experiment employing randomization was conducted to see what percentage of rats would show

empathy toward fellow rats in distress. Of the 30 total rats in the study, 23 showed empathy. Use the

bootstrap distribution to find a 99% confidence interval for the population proportion.

5

Question 6 (20 Points)
a. State the Central Limit Theorem for Means and explain the ideas behind it.

b. Describe the process of making a sampling distribution.

c. What is a point estimate? Discuss how point estimates create confusion for people reading

articles and scientific reports.

d. What conditions should be met to ensure that a sampling distribution of sample proportions is

normal?

Question 7 (5 Points)
State the assumptions for a one-population variance or standard deviation confidence interval.

6

Question 8 (5 Points)
Use the following formulas to identify the sample statistic (p-hat or x-bar or s) and the margin of error.

𝑆𝑎𝑚𝑝𝑙𝑒 𝑆𝑡𝑎𝑡𝑖𝑠𝑡𝑖𝑐 =
(𝑈𝑝𝑝𝑒𝑟 𝐿𝑖𝑚𝑖𝑡 + 𝐿𝑜𝑤𝑒𝑟 𝐿𝑖𝑚𝑖𝑡)

2

𝑀𝑎𝑟𝑔𝑖𝑛 𝑜𝑓 𝐸𝑟𝑟𝑜𝑟 =
(𝑈𝑝𝑝𝑒𝑟 𝐿𝑖𝑚𝑖𝑡 − 𝐿𝑜𝑤𝑒𝑟 𝐿𝑖𝑚𝑖𝑡)

2

A 95% confidence interval estimate of the population proportion of pies in a county fair in Ohio is

(0.46, 0.52).

Question 9 (20 Points)
Type I and II Errors

Scenario I:
Mike and his advertisement team have created an advertisement plan for a new flavor of soda. Right

now, approximately 16% of soda drinkers are purchasing this flavor. Mike needs to show his bosses that

his advertisement plan will increase the percentage of soda drinkers purchasing this new flavor. If Mike’s

advertising team succeeds in increasing the percentage of customers that prefer this new flavor, then

the company will increase supply and make more of the soda to meet demand. If not, then the company

will keep the supply as it currently is. After the advertising changes, Mike takes a random sample of

customers to determine if the percentage of soda drinkers that like the new flavor has increased. (They

are currently using a 5% significance level).

𝐻0: 𝜋 = 0.16 (𝑇ℎ𝑒 𝑐𝑜𝑚𝑝𝑎𝑛𝑦 𝑤𝑖𝑙𝑙 𝑛𝑜𝑡 𝑖𝑛𝑐𝑟𝑒𝑎𝑠𝑒 𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝑜𝑓 𝑡ℎ𝑒 𝑛𝑒𝑤 𝑓𝑙𝑎𝑣𝑜𝑟 𝑜𝑓 𝑠𝑜𝑑𝑎. )

𝐻𝐴: 𝜋 > 0.16 (𝑇ℎ𝑒 𝑐𝑜𝑚𝑝𝑎𝑛𝑦 𝑤𝑖𝑙𝑙 𝑖𝑛𝑐𝑟𝑒𝑎𝑠𝑒 𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝑜𝑓 𝑡ℎ𝑒 𝑛𝑒𝑤 𝑓𝑙𝑎𝑣𝑜𝑟 𝑜𝑓 𝑠𝑜𝑑𝑎. )

a. Write a description of a type 1 error and the possible consequences of that error in the context

of the problem.

b. Write a description of a type 2 error and possible consequences of that error in the context of

the problem.

c. Would you recommend any changes to the significance level or sample size based on what you

know about the type 1 and type 2 errors in this problem? Explain.

Scenario II:
A global sportswear company is contemplating contributing money to a political candidate in the next

election. The managers of the company do not want to contribute unless they are sure the candidate

will get the majority of the population vote and win the election. Otherwise, the company will not

contribute to the candidates’ campaign. (They are currently using a 10% significance level).

𝐻0: 𝜋 ≤ 0.5 (𝑇ℎ𝑒 𝑐𝑜𝑚𝑝𝑎𝑛𝑦 𝑤𝑖𝑙𝑙 𝑛𝑜𝑡 𝑐𝑜𝑛𝑡𝑟𝑖𝑏𝑢𝑡𝑒 𝑡𝑜 𝑡ℎ𝑒 𝑝𝑜𝑙𝑖𝑡𝑖𝑐𝑎𝑙 𝑐𝑎𝑛𝑑𝑖𝑑𝑎𝑡𝑒𝑠
′ 𝑐𝑎𝑚𝑝𝑎𝑖𝑔𝑛. )

𝐻𝐴: 𝜋 > 0.5 (𝑇ℎ𝑒 𝑐𝑜𝑚𝑝𝑎𝑛𝑦 𝑤𝑖𝑙𝑙 𝑐𝑜𝑛𝑡𝑟𝑖𝑏𝑢𝑡𝑒 𝑡𝑜 𝑡ℎ𝑒 𝑝𝑜𝑙𝑖𝑡𝑖𝑐𝑎𝑙 𝑐𝑎𝑛𝑑𝑖𝑑𝑎𝑡𝑒𝑠
′ 𝑐𝑎𝑚𝑝𝑎𝑖𝑔𝑛. )

7

a. Write a description of a type 1 error and the possible consequences of that error in the context

of the problem.

b. Write a description of a type 2 error and possible consequences of that error in the context of

the problem.

c. Would you recommend any changes to the significance level or sample size based on what you

know about the type 1 and type 2 errors in this problem? Explain.

Statistics homework help

1

4

Statistical Project –Part #3

Student’s Name

Institutional affiliation

Part #3; Hypothesis Testing

Hypothesis testing is a statistical test procedure that uses a random sample data to evaluate the plausibility of a tentative statement and then reliably extrapolate the observed results about the broader population (Warner, 2012). In particular, it is a process of finding out whether there is enough statistical evidence for us to be statistically confident to reject the null hypothesis. In this scenario, our testable claim is; “Is there a difference in the number/rate of bird strikes according to each phase of flight? The research or null hypothesis is; There is not a difference in the number of bird strikes in the phases of flight. To test the null hypothesis that the number of strikes are not different among the seven height bands, I will perform Chi square analysis. The data is from the FAA’s National Wildlife Strike Database for Civil Aviation (Dolbeer et al., 2021). The data reports from January 1990–December 2020, including even bird collisions with U.S. registered aircrafts in foreign countries.

I. Null and Alternative Hypothesis

Null hypothesis; There is not a difference in the number of bird strikes in the phases of flight

Alternative hypothesis; There is a significant difference in the number of bird strikes at different phases.

II. Significance Level: The alpha level is 0.05

III. Test Statistic

Under Ho, the test statistic for chi-square goodness of fit test;

image1.wmf

Iv.). Test Decision. The P-values are less than 0.0000. Since, the p-value is less than the alpha level, 0.05, we reject the null hypothesis. A p-value of less than the alpha of 5% indicates a strong evidence against the 5% probability that the null hypothesis is true (Warner, 2012).

image2.emf

v.). Conclusion. At 5% significance level, we can conclude that the number of bird strikes are statistically different at the phases of flight. The number of bird strikes across the seven height bands are statistically different in commercial, and general aviation aircrafts.

References

Dolbeer, R. A., Begier,M.J., Miller,P.R., Weller,J.R.,& Anderson, A.L.,(2021). Wildlife strikes

to civil aircraft in the United States, 1990-2020. Serial Report No. 26 .U.S.Federal

Aviation Administration, Office of Airport Safety and Standards, & Certification, Washington,DC.,USA.https://www.faa.gov/airports/airport_safety/wildlife/media/Wildlife-Strike-Report-1990-2020.pdf

Warner, R. M. (2012). Applied statistics: From bivariate through multivariate techniques:

From bivariate through multivariate techniques. SAGE.

_1713621098.unknown

Statistics homework help

Week One Journal

Course Reflection

Provide reflection of this week that contains 1 paragraph, which address at least one or two of the following topics:

Use the chapter power points to answer the topics below.

· Learning (i.e., information learned from course and/or content)

· Likes (i.e., liked most about the course and/or content)

· Dislikes (i.e., liked least about the course and/or content)

· Suggestions (i.e., suggestions for improvement about the course, content and/or assignments)

Statistics homework help

AME 500B
Final Exam
(3 Hours)

5/10/20

Before beginning any problem, read the entire exam. Do the problem
that seems simplest first. Please begin each problem on a separate
page of your own paper. Open book and notes, but no internet. Submit
to Final Submission Box

(20) 1. Consider the following wave equation for an infinite string:

( )
2 2

2
2 2 , 0c u x tt x

 ∂ ∂
− = ∂ ∂ 

.

Using the coordinate transformation
,x ct x ctξ η≡ + ≡ −

show that
( ) ( )( )2 , , ,

0
u x tξ η ξ η

ξ η

=
∂ ∂

.

(15) 2. If ( ) ( ), 0u x f x= and
( ) ( )

0

,

t

u x t
g x

t
=


=


, show the solution to the wave

equation of Problem 1 is

( ) ( ) ( ) ( )1 1,
2 2

x ct

x ct
u x t f x ct f x ct dt g t

c

+

′ ′= + + − +   ∫ .

(20) 3. Solve the wave equation

( )
2 2

2
2 2 , 0c u x tt x

 ∂ ∂
− = ∂ ∂ 

subject to the boundary conditions
( ) ( )0, , 0u t u L t= =

and initial conditions

( ) ( ) ( ) ( )
0

, 0
, 0 ,

t

u x
u x f x g x

t
=


= =

to show that the solution satisfies
( ) ( ) ( ), vu x t x ct w x ct= + + − .

(10) 4. Is the polynomial
2 2( , ) 2P x y x y ixy= + −

analytic? What two changes will make this polynomial analytic?

(15) 5. If f(z) is an analytic function, show that

( ) ( ) ( )
22

2
f z f z f z

x y

  ∂ ∂   ′+ =   ∂ ∂     
.

Hint: ( ) vuf z i
x x
∂ ∂

′ = +
∂ ∂

(10) 6. Criticize the following argument: Since

1

0

1

1 ;
1

k

k

k

k

z
z

z
z

z
z

=


=

=

= +

therefore

0
1 1

z z
z z
+ =

− −
.

(20) 7. Evaluate the following integral for k < 1:

( )
2

0

1
1 cos

I d
k

π

θ
θ

=
+  

∫ .

(20) 8. Consider the following Sturm-Liouville problem:

( ) ( )2 0, 0 1
d xd

x k x
dx dx

β φ φ β
 

+ = < < 
 

.

satisfying homogeneous BC. State at least 7 features of the solution that are known
without having to solve the equation.

(25) 9.a. Directly from the solution of the following 2-D heat transfer equation:

( )
2 2

2 2 , , 0, 0 , 0u x y t x a y bt x y
 ∂ ∂ ∂

− − = < < < < ∂ ∂ ∂ 

with homogeneous BC
( ) ( )
( ) ( )
0, , , , 0

, 0, , , 0

u y t u a y t

u x t u x b t

= =

= =

and IC
( ) ( ) ( ), , 0u x y f x g y= ,

show that
( ) ( ) ( )1 2, , , ,u x y t u x t u y t= ,

where

( )

( ) ( )
( ) ( )

( )

( ) ( )
( ) ( )

2

12

1 1

1

2

22

2 2

2

, 0, 0 ;

0, 0, , 0

, 0

, 0, 0

0, 0, , 0

, 0 .

u x t x a
t x

u t u a t

u x f x

u y t y b
t y

u t u b t

u y g y

 ∂ ∂
− = < < ∂ ∂ 

= =

=

 ∂ ∂
− = < < ∂ ∂ 

= =

=

b. Predict what the solution will be for 3D with the same BC in the third

dimension and a corresponding product IC.

Statistics homework help

Pugh Method Example: Design of a Car Horn
© 2006, Edward Lumsdaine and Monika Lumsdaine

This teaching example was originally developed by Professor Stuart Pugh. When it has
been used in workshops with engineers, the same design always emerges as superior, even
when very different groups conduct the evaluation. The following text describing this
example is taken from Creative Problem Solving: Thinking Skills for a Changing World,
College Custom Series, McGraw-Hill, 1993. We have made some changes from the
original version by Professor Pugh, since we are using it as an illustration, not an
evaluation exercise. Also, this example only includes the first round of evaluation.

Professor Pugh’s example is used by several authors who teach the Pugh method in their
design texts. We have rearranged and simplified the example to bring out some points we
want to make more clearly. The datum is a widely used car horn (in the 1990’s). Table 1
gives a list of design and performance criteria for the horn; these criteria are expressed not
just as quantitative targets but as positive goals. They are stated in broad terms and ranges,
not in restrictive detail. At this point, they have not been ranked according to importance.

Eight different conceptual designs were developed with this set of criteria. Two new
designs were added to the matrix during the first round of evaluation. These concepts are
shown in Table 2. Table 3 shows the completed Round 1 design evaluation matrix for the
car horn. This matrix includes the additions to the list of criteria. Design #1 is the datum
(the “best” existing product); it is entered in the first column next to the list of criteria.
Each new design concept was then evaluated against the datum for each criterion.

TABLE 1: Design Criteria for Automobile Horn

Original List of Criteria
Ease of achieving 100 – 125 decibel (sound level)
Ease of achieving 2000 – 5000 Hertz (sound frequency)
Resistance to corrosion (water, pollutants)
Resistance to vibration, shock, acceleration/deceleration, wear-and-tear
Resistance to temperature cycling and extremes
Low power consumption
Ease of maintenance
Small size
Long service life
Low manufacturing cost
Ease of installation
Long shelf life

Criteria Added During the Round 1 Discussion
Quick response time
Small number of parts—simplicity of design
Ease of operation (accessibility, emergency response)
Ease of integration into the automobile subsystems
Low weight

TABLE 2

TABLE 3

Discussion of the Results of Round 1

When the Round 1 evaluation has been completed for each concept, we can take a
general look at the results to judge the validity of the criteria. This is an important step
that must not be skipped. In the example, we notice that not one of the new concepts was
able to improve on the datum (or existing design) for resistance to vibration and
resistance to temperature changes; none was able to achieve smaller size or longer shelf
life. If one or more of these four criteria were important consumer requirements (with
many complaints and warranty claims), the designers would have to do more creative
thinking to come up with ideas that would address these concerns.

What happens during this first round of evaluation is much discussion about the criteria
and what they really mean. A consensus may emerge about which criteria are the most
important and should be given more weight than others. In the example, shelf life and
size may be insignificant parameters—in this case, they could be eliminated from further
consideration. On the other hand, quick response time, low weight, and small number of
parts were found to be important and were therefore added to the list, as were ease of
operation (especially during an emergency) and ease of integration of the horn into the
car’s systems (under the hood, in the steering column, and in the electrical system).

Can the students think of other important criteria (as customers)? For example, should
the horn be operable when the ignition is off? Some years ago, we had someone back
into our car while it was parked and we were sitting in it—there was not enough time to
start the ignition, and without the engine running, the horn did not work. The result was a
big dent and inconvenience for the repair and insurance claim.

Next, the total scores for each design are obtained. The positives and negatives are added
separately since positives cannot cancel out negatives. The results from Round 1 show
that some concepts were able to improve on the existing design; however, all concepts
accumulated a large number of negative marks. Therefore, the next activity concentrates
on making the concepts better by trying to eliminate as many of the negatives as possible.
Concept #6 was expanded into two additional versions (#9 and #10), where Concept #9
has only one negative—high manufacturing cost. This may not matter if this horn is for a
luxury car; if it is for an economy model, additional creative thinking may be able to
reduce the cost. If low manufacturing cost is very important and cannot be reduced for
this design, then other concepts that do not have this barrier need to be optimized further.

Although a team may decide to quickly throw out a few of the low-scoring concepts, this
should be done with caution. Some of the better features or improved components of
these concepts may be merged with other concepts for a better design. They should be
examined for stepping stone ideas; thus they provide a valuable service. During this
review and discussion of each design in an effort to make improvements, amended or
new concepts are added to the evaluation matrix as new designs. This process may occur
during the first meeting, or new concepts can be developed after an incubation period
over several days. The later concepts would then be evaluated in Round 2.

This concludes the car horn example. A Kitchen Lighting Example in three rounds is
given in the Entrepreneurship book by Lumsdaine & Binks and is available in
PowerPoint upon request (see www.InnovationToday.biz for ordering information).

Statistics homework help

Chapter 3

Quantifying the Extent of Disease

Learning Objectives

Define and differentiate prevalence and incidence

Select, compute, and interpret the appropriate measure to compare the extent of disease between groups

Compare and contrast relative risks, risk differences, and odds ratios

Compute and interpret relative risks, risk differences, and odds ratios

Critical Components of RCT

Randomization

Control group – ethical issues

Monitoring

Interim analysis

Data and safety monitoring board

Data management

Reporting

Prevalence

Proportion of participants with disease at a particular point in time

Example 3.1.
Computing Prevalence

Prevalence of CVD = 379/3799 = 0.0998 = 9.98%

Prevalence of CVD in Men = 244/1792 = 0.1362 = 13.62%

Prevalence of CVD in Women = 135/2007 = 0.0673 = 6.73%

Example: H1N1 Outbreak

H1N1 outbreak first noticed in Mexico.

Large outbreak early on in La Gloria—a small village outside of Mexico City

Studied extensively in the first report on H1N1 (Fraser, Donelly, et al. “Pandemic potential of a strain of Influenza (H1N1): Early findings,” Science Express, 11 May 2009.)

Important questions

Who is most likely to be impacted?

What are characteristics of people commonly impacted?

Age No ILI ILI Total
≤ 44 years 703 522 1225
> 44 years 256 94 350
Total 959 616 1575

Data on H1N1 outbreak in La Gloria, Mexico: n = 1575 villagers (out of 2155) were surveyed to determine if they had influenza-like illness (ILI) between 2/15/09 and 4/27/09.

Computing Prevalence (1 of 2)

Computing Prevalence (2 of 2)

Age No ILI ILI Total
≤ 44 years 703 522 1225
> 44 years 256 94 350
Total 959 616 1575

Prevalence of ILI = 616/1575 = 0.3911 = 39.11%

Prevalence of ILI in ≤ 44 = 522/1225 = 0.4261 = 42.61%

Prevalence of ILI in > 44 = 94/350 = 0.2686 = 26.86%

Incidence

Likelihood of developing disease among persons free of disease who are at risk of developing disease

Computing Incidence

Cumulative incidence requires complete follow-up on all participants.

Person-time data is used to take full advantage of available information in incidence rate.

Incidence rate often expressed as an integer per multiple of participants over a specified time.

Incidence of CVD?

Incidence Rate

Incidence of CVD

Incidence = 2/(10 + 9 + 3 + 10 + 5) = 2/37

= 0.054

5.4 per 100 person-years

Example 3.2.
Computing Incidence

Develop CVD Total Follow-Up Time (years)
Men 190 9984
Women 119 12153
Total 309 22137

Incidence Rate of CVD in Men = 190/9984 = 0.01903

= 190 per 10,000 person-years

Incidence Rate of CVD in Women = 119/12153 = 0.00979

= 98 per 10,000 person-years

Computing Incidence

Developed ILI Total Follow-Up Time (years)
≤ 44 years 522 20,064
> 44 years 94 3,514
Total 616 23,578

Incidence Rate of ILI in ≤ 44 = 522/20,064 = 0.0260

= 260 per 10,000 person-years

Incidence Rate of ILI in > 44 = 94/3514 = 0.0268

= 268 per 10,000 person-years

Risk difference (excess risk)

Comparing Extent of Disease
Between Groups (1 of 2)

Comparing Extent of Disease
Between Groups (2 of 2)

Risk difference of prevalent CVD in smokers versus nonsmokers

= 81/744 – 298/3055 = 0.1089 – 0.0975 = 0.0114

Population Attributable Risk of CVD in Smokers vs. Nonsmokers

= (0.0998 – 0.0975) / 0.0998 = 0.023 = 2.3%

Risk difference of history of ILI in males and females in La Gloria

No ILI ILI Total
Males 517 260 777
Females 442 356 798
Total 959 616 1575

= 356/798 – 260/777 = 0.4461 – 0.3346 = 0.1115

Comparing Extent of Disease
Between Groups (1 of 7)

Relative risk

Comparing Extent of Disease
Between Groups (2 of 7)

Comparing Extent of Disease
Between Groups (3 of 7)

Relative risk of CVD in smokers versus nonsmokers

= 0.1089/0.0975 = 1.12

Relative risk of ILI in females versus males

No ILI ILI Total
Males 517 260 777
Females 442 356 798
959 616 1575

= 0.4461/0.3346 = 1.33

Comparing Extent of Disease
Between Groups (4 of 7)

Odds ratio

Comparing Extent of Disease
Between Groups (5 of 7)

Odds ratio of CVD in hypertensives versus hypertensives

Comparing Extent of Disease
Between Groups (6 of 7)

Comparing Extent of Disease
Between Groups (7 of 7)

Odds ratio of ILI in younger group versus older group

Age No ILI ILI Total
≤ 44 years 703 522 1225
> 44 years 256 94 350
Total 959 616 1575

Relative Risks and Odds Ratios

Not possible to estimate relative risk in case-control studies

Possible to estimate odds ratio because of its invariance property

Case-control study to assess association between smoking and cancer

Invariance Property of Odds Ratio
(1 of 2)

Invariance Property of Odds Ratio
(2 of 2)

Odds ratio for cancer in smokers versus nonsmokers

= (40/29) / (10/21) = 2.90

Odds of smoking in patients with cancer versus not

= (40/10) / (29/21) = 2.90(!)

Statistics homework help

1

4

Statistical Project –Part #3

Student’s Name

Institutional affiliation

Part #3; Hypothesis Testing

Hypothesis testing is a statistical test procedure that uses a random sample data to evaluate the plausibility of a tentative statement and then reliably extrapolate the observed results about the broader population (Warner, 2012). In particular, it is a process of finding out whether there is enough statistical evidence for us to be statistically confident to reject the null hypothesis. In this scenario, our testable claim is; “Is there a difference in the number/rate of bird strikes according to each phase of flight? The research or null hypothesis is; There is not a difference in the number of bird strikes in the phases of flight. To test the null hypothesis that the number of strikes are not different among the seven height bands, I will perform Chi square analysis. The data is from the FAA’s National Wildlife Strike Database for Civil Aviation (Dolbeer et al., 2021). The data reports from January 1990–December 2020, including even bird collisions with U.S. registered aircrafts in foreign countries.

I. Null and Alternative Hypothesis

Null hypothesis; There is not a difference in the number of bird strikes in the phases of flight

Alternative hypothesis; There is a significant difference in the number of bird strikes at different phases.

II. Significance Level: The alpha level is 0.05

III. Test Statistic

Under Ho, the test statistic for chi-square goodness of fit test;

image1.wmf

Iv.). Test Decision. The P-values are less than 0.0000. Since, the p-value is less than the alpha level, 0.05, we reject the null hypothesis. A p-value of less than the alpha of 5% indicates a strong evidence against the 5% probability that the null hypothesis is true (Warner, 2012).

image2.emf

v.). Conclusion. At 5% significance level, we can conclude that the number of bird strikes are statistically different at the phases of flight. The number of bird strikes across the seven height bands are statistically different in commercial, and general aviation aircrafts.

References

Dolbeer, R. A., Begier,M.J., Miller,P.R., Weller,J.R.,& Anderson, A.L.,(2021). Wildlife strikes

to civil aircraft in the United States, 1990-2020. Serial Report No. 26 .U.S.Federal

Aviation Administration, Office of Airport Safety and Standards, & Certification, Washington,DC.,USA.https://www.faa.gov/airports/airport_safety/wildlife/media/Wildlife-Strike-Report-1990-2020.pdf

Warner, R. M. (2012). Applied statistics: From bivariate through multivariate techniques:

From bivariate through multivariate techniques. SAGE.

_1713621098.unknown

Statistics homework help

Reliability Modelling

Series Systems

Parallel Systems

Bayesian Testing

Design Verification

Design for Six Sigma roadmap

HoQ1→Boundary→HoQ2→P-diagram→DFMEA→PFMEA→SCIF→Control plan

HoQ1→Boundary→HoQ2→P-diagram→DFMEA→PFMEA→SCIF→Control plan

HoQ1→Boundary→HoQ2→P-diagram→DFMEA→PFMEA→SCIF→Control plan

HoQ1→Boundary→HoQ2→P-diagram→DFMEA→PFMEA→SCIF→Control plan

System validation plan

System verification plan

Sub-system verification plan

Component verification plan

Time line

System

Sub-
system

Component

System

Sub-
system

Slide 6

What do I Verify & Validate?

Slide 7

Pool is 50 metres long

500 metres

DfSS Process

Boundary
diagram

Parameter
diagram

Design
FMEA

SCIF

HoQ #1

Process
FMEA

SCIF
Manufacturing
control plan

Field
performance

Project goals

System boundary diagram

Slide 9

Angle
mechanism

Velocity
mechanism

Support

Barrel

Distance
(475 – 525 m)

Angle
43o – 47o

Velocity (m/s)
75.5 – 79.2

Gravitational
acceleration
(m/sec2)
9.81 – 9.82

Sound
(100 – 120 dB)

Height
(> 90 m)

Sound
mechanism

Pool

Side Show
Bob

( ) 
g

2sinv
d

2
θ

=
( )
2g

sinv
h

22
θ

=

Velocity mechanism boundary diagram

Slide 10

Support
Inner barrel

wall

Spring constant

Weight

Friction
coefficient

Distance
compressed

v =
f(spring constant,
friction coefficient,
weight, distance
compressed)

Rollers Plunger Spring

Compression
lever

Compression
gauge

Side Show
Bob

Velocity (m/s)
75.5 – 79.2

Spring boundary diagram

Slide 11

Spring constant

Wire diameter

Free length

Number of
active windings

Young’s modulus

Force =
f(Young’s modulus, wire diameter, free length, number of
active windings, Poisson ratio, outer diameter)

Poisson ratio

Outer diameter

Bogey test

• The duration for a Bogey test is equal to the reliability requirements
being demonstrated.
• For example, if a test is designed to demonstrate that a component has specific reliability at

100 hours means the test duration is
100 hours, then the test is designated as a Bogey test.

• Example 1: If 95% reliability is required at 200,000 kilometres of service, then the units being
tested will be removed from testing when they fail or when they complete the equivalent of
200,000 kilometres of testing. The sample size required to demonstrate reliability of r with a
confidence level of c is:

Bogey: a numerical standard of performance set up as a mark
to be aimed at especially in competition.

ln(r)

c)ln(1
N


=

Slide 12

Calculation of test sample size

Reliability Confidence Sample Size

99% 95% 299

99% 90% 229

99% 50% 69

95% 95% 59

95% 90% 45

95% 80% 31

90% 90% 22

90% 80% 16

Example 2: A windshield wiper motor must demonstrate 99% reliability with 90%
confidence at 2 million cycles of operation. How many motors must be
tested to 2 million cycles with no failures to meet these requirements:

Following table shows relationship between sample size, confidence interval & reliability

229
ln(r)

c)ln(1
N =


=

Slide 13

Do tested parts represent the population?

• Variation from multiple production operators

• Variation from multiple lots of raw materials

• Variation from tool wear

• Variation from machine maintenance

• Variation from seasonal climatic changes

• Variation from supplier changes

Slide 14

Does the test represent actual use?

• Number of cycles

• Environment

• Variability in the part itself

Slide 15

What are the design requirements

• Application environment is harsh and highly variable
• Vehicles must operate reliably in artic conditions and in desert conditions

• Driving profiles range from the 16 year-old male to the 90 year-old female

• An airliner may fly long haul ocean routes for 20 years

• Identical model flies short-range routes resulting in many more take-offs

• Combining this variety into a realistic test is difficult
• Consider specific tests aimed at particular failure causes or failure modes

• Ensure component requirements are properly linked to the system
requirements

Slide 16

95th percentile customer

• 95th percentile of what?
• Cycles

• Cold temperature

• Hot temperature

• Salt

• Automobile engine
• Starts

• Run time

Slide 17

Percentile vs. cycles

0

100

200

300

400

500

600

700

800

900

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Percentile

B
ra

ke
A

p
p

li
ca

ti
o

n
s

(T
h

o
u

sa
n

d
s)

Slide 18

Randomise loads

Slide 19

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Deceleration (g-force)

P
ro

b
a

b
il

it
y

D
e

n
si

ty

Average Customer

95th Percentile Customer

Bayesian Weibull

• Bogey test is inefficient. By extending the test duration beyond the required life, the total
time on test can often be reduced. When the test duration is extended, it is necessary to
make assumptions concerning the shape of distribution of the time to fail.

• In Bayesian testing this is done by assuming a Weibull distribution for time to fail and by
assuming a shape parameter

• Assume β is known:
• β is dependent on the physics of failure
• Year to year re-qualification

• Programme to programme

• Old design to new design

• Time raised to β is an exponential random variable
• Reduces testing requirements

Slide 20

Effect of shape parameter on Time-to-Fail
Weibull slope β (shape) = 3.6

4.03.63.22.82.42.01.61.20.80.40.0

400

300

200

100

0

Bogeys

F
r
e

q
u

e
n

c
y

Shape 3.6

Scale 2

N 2500

Weibull

Histogram of Time-to-Fail

Slide 21

Effect of shape parameter on Time-to-Fail
Weibull slope β (shape) = 1

80706050403020100

900

800

700

600

500

400

300

200

100

0

Bogeys

F
r
e

q
u

e
n

c
y

Mean 15

N 2500

Histogram of Time-to-Fail
Weibull Shape Parameter = 1

Slide 22

Effect of shape parameter on Time-to-Fail
Weibull slope β (shape) = 1.8

14.212.811.29.68.06.44.83.21.60.0

350

300

250

200

150

100

50

0

Bogeys

F
r
e

q
u

e
n

c
y

Shape 1.8

Scale 5

N 2500

Weibull

Histogram of Time-to-Fail

Slide 23

Effect of shape parameter on Time-to-Fail
Weibull slope β (shape) = 8

1.91.71.51.31.10.90.70.5

600

500

400

300

200

100

0

Bogeys

F
r
e

q
u

e
n

c
y

Shape 8

Scale 1.4

N 2500

Weibull

Histogram of Time-to-Fail

Slide 24

Bayesian test design
• Tests are designed to demonstrate a specific reliability at a specific

time (R95/C90 at 100,000 miles).

• To have 95% reliability at 100,000 miles the mean must be
• greater than 1,500,000 miles if b = 1.0

• greater than 330,000 miles if b = 1.8

• greater than 220,000 miles if b = 3.6

• greater than 140,000 miles if b = 8.0

Slide 25

Bayesian test design

• Supported and encouraged by Automotive Industry.

• Bogey Testing is the most inefficient method of testing.
• If 95% reliability is required with 90% confidence at 100 hours, there is no less efficient

method than designing a test for a duration of
100 hours.

• Use extended testing.

Slide 26

Sample size to achieve R95/C90 at 1 Bogey
b: shape parameter 1 Bogey 2 Bogeys 3 Bogeys

1.0 45 22 15

1.2 45 20 12

1.5 45 16 9

2.0 45 11 5

3.5 45 4 1

7.0 45 1 1

Slide 27

Sample size to achieve R90/C90 at 1 Bogey
b: shape parameter 1 Bogey 2 Bogeys 3 Bogeys

1.0 22 11 8

1.2 22 10 6

1.5 22 8 5

2.0 22 6 3

3.5 22 2 1

7.0 22 1 1

Slide 28

Establishing the shape parameter (b)

• Can be based on physics of failure

• Should be based on (at least) 7 failures

• Can also be based on experience

• There should be a policy to build an internal database

Slide 29

Other benefits

• Failure modes will be known

• Testing can be accelerated

• Designs can be compared

• Component failures can be catalogued

• Degradation testing may be possible

• Cost savings because we understand the limits of the design

Slide 30

Example test duration

• R95/C90 at 1.5 million miles means

• to have 95% reliability at 100,000 (i.e. L5 = 1.2 million miles), with 90%
confidence.

• If the Weibull slope b = 7.04 and the sample size = 8. What is the test
duration?

• If 1 unit fails at time = 1.82 million miles does the product fail to
demonstrate the required reliability?

Slide 31

Example test duration

Slide 32

• One unit fails after 1.82 million cycles
• How long do the remaining 7 units have to survive to meet the original

test requirements?

Example

• Assume: The requirements are not met.

• Remember that the width of the confidence limits decrease as the
sample size and test duration increase.

• You must make a decision:
• Does the product fail to meet the requirements with this small sample size, or

• Is the product not durable enough

Slide 33

Example

• There are several options
• Continue testing the surviving items

• Test additional items

• Re-design and re-test

• For extended test plans (beyond 1 lifetime) it is common to obtain
failures
• Failures beyond 1 lifetime do not necessarily indicate a poor design

<BayesianTestingTemplate.xls>

Slide 34

• Does a basketball player have a 90% free throw percentage?

• Verify free throw percentage with 85% confidence

• Acceptance test requires
• 18 consecutive successful free throws

• If the player’s free throw percentage is exactly 90%
• The probability of passing the test is

Probability of passing a bogey test

15.09.0
18

==p

• Demonstrate a reliability of 95% at 10 years with a confidence level of
90%

• System has a time to fail distribution for a system with
a Weibull shape parameter of 2.5

• Four systems have to be tested for 26.3 years without failure

Probability of passing a Bayesian test

( ) 

( )

( ) ( ) 1.0563.0Test Passing

563.03.26

81.32
95.0ln

10

4

81.32

3.26

5.2/1

5.2

==

=

=

=

=




P

eR

• 45 units with 95% reliability at 100 time units
• β = 2

• θ = 441.54

• To demonstrate 95% reliability with 90% confidence
• 45 units surviving to 100 time units

• 11 units surviving to 202 time units

• 5 units surviving to 300 time units

• Compute the probability of passing each of the 3 tests above

Zero failure test plan problems

<ProbabilityOfPassingTest.xls>

Probability of passing a test – β = 2

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

5 15 25 35 45 55 65 75 85

True L5 Life (Years)

P
ro

b
a

b
il

it
y

o
f

P
a

s
s

in
g

T
e

s
t

Probability of
passing test is
1 – confidence

Probability of passing a test

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

5 15 25 35 45 55 65 75 85

True L5 Life (Years)

P
ro

b
a
b

il
it

y
o

f
P

a
s
s
in

g
T

e
s
t

b = 1.5

b = 2.5

b = 3.5

b = 5

Confidence interval width

0 1 2 3 4 5 6 7

1

2

3

N
u

m
b

e
r

o
f

F
a

il
u

re
s

Confidence Interval Width (# of Bogeys)

b = 1.5

b = 2.5

• Statistically designed test can be defeated by selecting the parts in a non-random manner

• Select parts that are close to the nominal dimension

• The variability is reduced

• Positive bias is introduced because the parts close to nominal will perform better than those
further than nominal

• Combination of reduced variability and positive bias greatly improves the probability of
passing the test

• Select parts at worst case tolerance combinations

• The variability is reduced

• Negative bias is introduced because the worst-case parts will perform worse than those
randomly selected

• Combination of reduced variability and negative bias greatly reduces the probability of
passing the test

Sensitivity to a random sample

• Desire to determine free throw percentage for all male high school
basketball players in Detroit

• Select the best free throw shooter from each team?
• Similar to building prototype parts to nominal

• Select the worst free throw shooter from each team?
• Similar to building prototype parts to worst case

• In either case a statistical test is nonsense

Sensitivity to a random sample

• Auction price for clocks along

• clock age

• number of bidders

• population is normally distributed
• mean = 1327

• standard deviation = 393

• population L5 = 681

• But what if the sample is not random?

• Five oldest clocks are selected

• 90% confidence interval for L5 is 831 to 1641

• true L5 of 681 falls outside this range

• selecting the oldest clocks is similar to making 5 prototype parts with a new tool

Sensitivity to a random sample

Sensitivity to a random sample

0 500 1000 1500 2000 2500

Price

P
ro

b
a

b
il

it
y
D

e
n

s
it

y

Age Greater Than 180

Entire Population

Test at Worst Case tolerance?

• What is worst case
• Nominal may be worst case

• Launching projectile at 45°

• Can you produce worst case?
Number of

Characteristics
Number of Tolerance

Combinations

2 4

3 8

4 16

5 32

10 1,024

20 1,048,576

50 1.13×1015

100 1.27×1030

Slide 45

0%

5%

10%

15%

20%

25%

20% 25% 30% 35% 40% 45% 50%

P
ro

b
a

b
il

it
y

o
f

A
ll

C
h

a
ra

ct
e

ri
st

ic
s

in
W

o
rs

t
C

a
se

R
e

g
io

n

Percentage of Tolerance Defined as Worst Case

2 Characteristics 3 Characteristics 4 Characteristics 5 Characteristics 6 Characteristics 7 Characteristics

Assumes Cpk = 1.33

Test design

• Use statistics as baseline

• Recommend sample size of 4 to 8
• Select samples as close to worst case as possible

• More samples if testing is inexpensive and sources of variation can be incorporated

• Less if testing is expensive

• Always ask if calculations can be substituted

• If one or more samples fail prior to Bogey test is failed

• If all samples exceed Bogey
• If one or two failures test is passed

• If more than two failures

• Compute reliability confidence limits and use an guideline

• Compute shape with confidence limits and use as guideline

Slide 48

Strategy

• Build confidence using a bottom up approach

• Short tests aimed at key failure modes or causes based on the P-diagram & FMEA

• Understand equations
• Test unknown areas

• Use models – FEA, SPICE, CATIA, etc.

• Use standard, validated components

• Focus on System Interaction

Slide 49

Statistics homework help

Kano, TRIZ, 6-3-5 & TRIZ

Slide 2

Why listen to the Voice of the Customer?

When to listen to Voice of the Customer

Slide 3

• Product / Service Idea

• Size of market
• Market characteristics
• Key buying factors

• Product or service technical features

• Verify customers
• Verify customer wants, needs and

expectations
• Prioritising these

• Translate wants/needs into Functional
Requirements

• Translate functional requirements into
design parameters and process variables

Market research

Market potential

Competitive
analysis

Initial
Customer
Research

Capturing/Verifying
Voice of the
Customer

Designing new
product / process to
meet customer
requirements

}

}
}

Customer research

Idea
generation

Slide 4

What is Voice of the Customer?

• Customer Wants

• Customer Needs

• Customer Demands

• Customer Requirements

• Customer Wishes

• Customer Delighters

• Customer Expectations

• Customer Critical to Satisfaction Items (CTSs)

Like any game, if you
know the rules better
than your competitor, you
have an advantage!

Does SKF know our
customers and potential
customers better than our
competition?

Whatever it is that will make customers come to you. That is what customer likes,

that is what you need to find out, that is Voice of the Customer!

Slide 5

• Whose needs specifically must be met for this product or process or service

to be successful?

• Are all customers equally important?

• Are there other potential key customers?

• Decision makers

• Administrators

• End users

• Maintenance

Protect SKF against competing customers

Identify customers

Your
Service
Process

Supplier

Supplier

Customer

Customer

Your organisation

Internal
Customers

Internal
Customers

INPUT OUTPUT

Slide 6

Who is the customer?

• If you sell Barbies to “Toys‘R’Us”, who’s the Customer?
• Toys‘R’Us?

• The mother who bought it?

• The child that plays with it?

• Since Toys‘R’Us is your direct customer do the others matter?

Hospital A 48.6%

Hospital B 40.9%

Be careful

Cancer survival rates

Total Kidney Liver

Hospital A 48.6% 36.7% 50.0%

Hospital B 40.9% 40.0% 54.0%

Cancer survival rates

Simpson’s paradox

Total Kidney Liver

Hospital A 48.6% 36.7% 50.0%

Hospital B 40.9% 40.0% 54.0%

Total Kidney Liver

Hospital A 272 560 22 60 250 500

Hospital B 327 800 300 750 27 50

Percentages

Counts

Slide 10

Sex discrimination at Berkeley

• The University of Berkeley some years back (1973) found evidence
that there was sex discrimination in admission to graduate school.

• It was observed that
(1) A smaller percentage of women were admitted to graduate school than men.

• But when the University looked more closely at the evidence, they
also found that:

(2) In each department, the percentage of women admitted is the same as the percentage
of men.

• How can (1) and (2) both be true?

• The answer is that this is an instance of Simpson’s paradox. But what
does that mean?

Actual lawsuit

Slide 11

Simpson’s paradox

Applicants Admitted

Men 8442 44%

Women 4321 35%

Men Women

Major Applicants Admitted Applicants Admitted

A 825 62% 108 82%

B 560 63% 25 68%

C 325 37% 593 34%

D 417 33% 375 35%

E 191 28% 393 24%

F 272 6% 341 7%

Kano

Slide 13

Why design a survey

• It is difficult to use surveys

• Without a design there is a high probability of obtaining misleading information

• Things that go wrong with surveys:
• The questions are not clear

• The respondent loses interest

• The results are in a form that is difficult to analyse

• Sample does not represent population

• Respondents do not represent the sample

Satisfaction as a function of need fulfilment

Slide 14

(Broken Process)
(Product Failure)

Dissatisfied
Feeling

Satisfied
Feeling

C
u

st
o

m
e

r
S

a
ti

sf
a

ct
io

n

Fulfilment Fulfilled
Condition

Unfulfilled
Condition

(Perfect Process)
(Product Performs)

y-axis is Customer
Satisfaction

x-axis is the degree to
which the desired service

or product is fulfilled

Three dimensions of customer needs

Slide 15

(Broken Process)
(Product Failure)

Dissatisfied
Feeling

Satisfied
Feeling

C
u

st
o

m
e

r
S

a
ti

sf
a

ct
io

n

Fulfilment Fulfilled
Condition

Unfulfilled
Condition

(Perfect Process)
(Product Performs)

Delighters

One-Dimensional

Must-Be
Basic Function

Slide 16

Kano questionnaire definitions

• Requirement type
• Must-be

• One-Dimensional

• Delighters

• Indifferent

• Reverse, Questionable

• Definition
• If the product does not have this no one will

be interested in it.

• The more you provide this function the more
satisfied the customer will be.

• The customer is happy when it is there but
will not complain if it is not there.

• The customer does not care about this
feature.

• Poor question wording, or under certain
circumstances, this particular function has a
negative interaction with other important
functions and we never really understood
what we were talking about.

Slide 17

Questionnaire development
• Develop a pair of questions for each potential

requirement.

• Two part questions

• How do you feel if the feature (or function) is present in the
product/service?

• How do you feel if the feature (or function) is NOT present in
the product/service?

• Multiple choice answer
1. I like it that way
2. It must be that way
3. I am neutral
4. I can live with it that way
5. I dislike it that way

Functional

Dysfunctional

Kano questionnaire example

How do you feel if your radio has

Bluetooth?

1. I like it that way

2. It must be that way

3. I am neutral

4. I can live with it that way

5. I dislike it that way

How do you feel if your radio

does not have Bluetooth?

1. I like it that way

2. It must be that way

3. I am neutral

4. I can live with it that way

5. I dislike it that way

Dysfunctional form of the
Question

Functional form of the
Question

Slide 19

Legend
D: Delighter I : Indifferent
M: Must-be R: Reverse
O: One-dimensional Q: Questionable result

Customer Dysfunctional
Requirements 1. Like 2. Must-Be 3. Neutral 4. Live With 5. Dislike

Functional Q D D D O
R I I I M
R I I I M
R I I I M

1. Like
2. Must-Be
3. Neutral
4. Live With
5. Dislike R R R R Q

Kano evaluation table

Slide 20

Kano evaluation table example

1. Collect and tally each of the paired customer responses into appropriate location
in Evaluation Table.

2. Highest number wins.

3. Ties normally indicate that additional information is required. You may be dealing
with 2 market segments, or you may need to ask questions about more detailed
customer requirements.

4. Large number of Q’s indicates that questions should be temporarily deleted until
confusion can be resolved.

5. Large number of R’s indicates marketplace thoughts are opposite of the creators.

Question M O D I R Q Total Grade
1 1 21 1 23 O
2 22 1 23 M
3 5 13 5 23 D
4 1 4 6 11 1 23 I
5 9 6 1 6 1 23 M
6 2 7 10 3 1 23 I

Slide 21

Graphical approach

1. Calculate Dissatisfaction and Satisfaction Indices:

2. Plot DI vs. SI (Kano diagram)




+++

+
−=

IDOM

OM
DI

IDOM

OD
SI

+++

+
=

Delighters gone wrong

• The Cadillac Fleetwood V8-6-4
• Cylinder deactivation to keep up with the CAFE standards

• Jerky ride

• Stalled often

• Toyota Auto Park

Slide 22

Slide 23

Web based survey case study

• US Automotive consumers given J.D. Power customer satisfaction survey

• Survey has large impact on vehicle sales

• Survey has no value for diagnosing problems and improving

• Question type

• How satisfied are you with your radio?

• How satisfied are you with your seats?

• Why don’t you like the radio?

• What can I change to make you like it?

Slide 24

Customer satisfaction survey

• 181,000 July and August 2000 buyers & lessees were requested to participate
at 3-4 months service

• 80 Vehicle lines included in survey

• 10,758 Surveys were completed

Slide 25

Customer satisfaction survey

• How satisfied are you with your radio?
• Satisfaction scale is 1 to 7

• If user answers 1, 2 or 3 they are given drill down questions
• Select one or more of the following radio problems

• Reception

• Volume

• Clarity

• Controls

• Etc.

• Drill down continues

• Open ended comments are allowed

• With no incentives the average response time was 45 minutes

Customer satisfaction survey
Customer Insight Diagnostic Survey
• #1 Instrument Panel complaint was customer wants an ashtray &

• lighter

• Make & Model and sample comments specifically related to not

• including ashtray & lighter as standard feature

• – Honda Civic (x8) “It costs extra for an ashtray and a cigarette lighter. I think that’s ridiculous”

• – Saturn SL2 (x2) “There is no ashtray or any receptacle for small trash items such as gum wrappers”

• – Toyota Avalon “Centre console needs wire slot for power plug to close lid”

• – Saturn SC“No ashtray or lighter”

• – Mercury Mystique “No ashtray”

• – Mazda 626 (x2) “Did not come standard with ashtray”

• – Honda Accord “No ashtrays”

• – Pontiac Bonneville “Need a car phone jack”

• – Cadillac Seville (x3) “Front ashtray/lighter not standard but should be in this class of car”

• – Mercury Villager “No ashtray”

• – Chrysler T&C “What ashtray”

• – Honda CRV “No cigarette lighter!”

Slide 26

Slide 27

Summary

• Planning and design of the survey is important to obtain meaningful results.

• Sample selection must ensure the population is adequately represented.

• Wording and order of questions and answer choices should be thought out to
increase response rate and accuracy.

• The analysis strategy must be considered upfront in the survey design.

• If the survey is designed well, conducting the survey and analysing the results
will be easy.

Triz & 6-3-5

TRIZ

• Theory of inventive problem solving

• Creativity by resolving conflicts

• Based on patent review

• www.TRIZ40.com

Slide 29

Brainwriting 6-3-5

• Provides a basic worksheet for team members to record their ideas.

• Leverages synergies between team members to develop the ideas that feed off of
each other.

• Worksheet helps to ensure repeatable results.

• Process:
• Assembly a team (six is an ideal number) and state the problem statement
• Have each of the six people write down (3) ideas on their individual worksheet within a five

minute time frame
• Write each idea as concise but in a complete sentence (one idea per box)

• At the end of the five minutes, everyone passes their individual worksheet to the person on
their left

• The next person reads the ideas written by the person before them and then is given five
more minutes to think of another (3) ideas – these new ideas can be spurred on by the
previous ideas list

• The process is repeated until each of the six people contribute to each sheet

Slide 30

Brainwriting 6-3-5

Problem Statement:

Person Idea 1 Idea 2 Idea 3

1

2

3

4

5

6

Pugh’s Concept Selection

Pugh’s method

• Creativity – a final opportunity to be creative
• Structured method to evaluate multiple alternatives in the concept development phase

• Capture best elements of concepts to synthesise better concepts

• Proactive team approach that creates change improvements in development versus
implementation process

• Increase team’s understanding of design capability

• Optimise development time and costs

Team participants using this process often:
• To achieve greater insight and awareness of possible solutions by

building on each others ideas
• To find that the method stimulates generation of new and better

concepts

Slide 33

Pugh’s concept selection: Process flow

Slide 34

Rate concept alternatives

Create hybrid concepts

Select reference concept

Create concept screening matrix

Reflection

time

Concept Selection

Number of Concepts

Choose criteria

• List requirements against which the concepts will be evaluated

• Final list should be unambiguous and must be agreed by the full team

• Target number of criteria is about 10. If you have more, focus on most important
requirements

• Ideally, use the functional and attribute requirements from QFD HOQ #1

Slide 35

Requirements Datum 1 2 3 4

Total +
Total –
Total S’s

Concepts

QFD
HoQ#1

Functional & Attribute

Characteristics (HOW’s)

Form screening matrix

Slide 36

Problems
(requirements)
on left vertical
axis

Concepts across the top horizontal

A + – + +

B + – + +

C – + – –

Tips:

A. Team discusses criteria (requirements or metrics) — “will

they distinguish one concept for another?”

B. Attach individual solution concepts across the top.

Example: Pugh concepts for car horn

Slide 37

Example: Pugh matrix for car horn

Slide 38

Statistics homework help

Week 1 Assignment


Adapted from Statistical Reasoning for Everyday Life (Bennett, Briggs, & Triola, 2017).

Understanding:

• Define the terms as they apply to statistical studies: sample, raw data, sample statistic, confidence interval, margin of error, census.

• Describe the five basic steps in a statistical study. Give an example of their application for a topic related to your research interests.

• Explain why the following statement is true: The 95% confidence interval for a poll suggested that support for Governor Garcia is between 55% and 60%. Therefore, we can be certain that a majority of the population supports the governor.

• Explain why this is false: One study of heart disease involved treating male physicians with daily doses of aspirin. Because the study concluded that aspirin helps males avoid heart disease, it follows that females can also avoid heart disease by taking aspirin.

• What is peer review, and why is it useful?

Application:

• In a Harris Interactive survey of 1006 adults, 86% say that they wash their hands after using a public restroom; the margin of error is 3 percentage points. USA Today reported that among 6028 adults observed in restrooms, 85% washed their hands; the margin of error is 1 percentage point. Use the given statistics and margin of error to identify the confidence interval for each study. Which study do you believe, and why?

• In a survey of 1002 people, 701 (70%) said that they voted in the last presidential election (based on data from ICR Research Group). The margin of error for this survey was 3 percentage points. However, actual voting records show that only 61% of eligible voters cast a vote. Does this imply that people lied when responding to the survey? Explain.

• Describe how you would apply the five basic steps in a statistical study to the following research question: determine the percentage of drivers who text while they are driving.

• The Journal of American Psychologists prints an article evaluating a new drug for depression. The researchers who wrote the article received funding for their labs from the pharmaceutical company that produces the drug. Is there a potential for bias in this research study? How could it be avoided? Explain your answer.

• A college dean obtains an alphabetical list of all full-time students at her college and selects every 50th name on that list to survey those students regarding the total amount of student loan debt that they will have upon graduating. She then reports this average (mean) amount of debt among these students as the average of all college students. What type of sample of this? What could she do to improve her sample?

• Explain any problems likely to cause confounding, and suggest how they could be avoided: in a comparison of gasoline with different octane ratings, 24 vans are driven with 87 octane gasoline, and 28 SUVs are driven with 91 octane gasoline. After each vehicle has been driven for 250 miles, the amount of gasoline consumed is measured.

• Explain which of the 8 guidelines for evaluating a statistical study might be most relevant: In a survey of 1,200 college students, each was asked whether they are a good person.

• The following presents a headline in a local newspaper, as well as the story summary. Discuss whether the headline accurately represents the story.

Headline: “Drugs Shown in 98% of Movies”

Story Summary: A “government study” claims that drug use, drinking, or smoking was depicted in 98% of top movie rentals (Associated Press).

• What crucial information is missing from the following “sound bite”? A USA Today “Snapshot” reported that the percentage of people with diabetes who don’t know that they have diabetes is “1 in 4.” The source was given as the American Diabetes Association.

• What crucial information is missing from the following “sound bite”? CNN reports on a Zagat survey of America’s top restaurants, which fund that “only 9 restaurants achieved a rare 29 out of a possible 30 rating, and none of these restaurants are in the Big Apple.”

Statistics homework help

Kano, TRIZ, 6-3-5 & TRIZ

Slide 2

Why listen to the Voice of the Customer?

When to listen to Voice of the Customer

Slide 3

• Product / Service Idea

• Size of market
• Market characteristics
• Key buying factors

• Product or service technical features

• Verify customers
• Verify customer wants, needs and

expectations
• Prioritising these

• Translate wants/needs into Functional
Requirements

• Translate functional requirements into
design parameters and process variables

Market research

Market potential

Competitive
analysis

Initial
Customer
Research

Capturing/Verifying
Voice of the
Customer

Designing new
product / process to
meet customer
requirements

}

}
}

Customer research

Idea
generation

Slide 4

What is Voice of the Customer?

• Customer Wants

• Customer Needs

• Customer Demands

• Customer Requirements

• Customer Wishes

• Customer Delighters

• Customer Expectations

• Customer Critical to Satisfaction Items (CTSs)

Like any game, if you
know the rules better
than your competitor, you
have an advantage!

Does SKF know our
customers and potential
customers better than our
competition?

Whatever it is that will make customers come to you. That is what customer likes,

that is what you need to find out, that is Voice of the Customer!

Slide 5

• Whose needs specifically must be met for this product or process or service

to be successful?

• Are all customers equally important?

• Are there other potential key customers?

• Decision makers

• Administrators

• End users

• Maintenance

Protect SKF against competing customers

Identify customers

Your
Service
Process

Supplier

Supplier

Customer

Customer

Your organisation

Internal
Customers

Internal
Customers

INPUT OUTPUT

Slide 6

Who is the customer?

• If you sell Barbies to “Toys‘R’Us”, who’s the Customer?
• Toys‘R’Us?

• The mother who bought it?

• The child that plays with it?

• Since Toys‘R’Us is your direct customer do the others matter?

Hospital A 48.6%

Hospital B 40.9%

Be careful

Cancer survival rates

Total Kidney Liver

Hospital A 48.6% 36.7% 50.0%

Hospital B 40.9% 40.0% 54.0%

Cancer survival rates

Simpson’s paradox

Total Kidney Liver

Hospital A 48.6% 36.7% 50.0%

Hospital B 40.9% 40.0% 54.0%

Total Kidney Liver

Hospital A 272 560 22 60 250 500

Hospital B 327 800 300 750 27 50

Percentages

Counts

Slide 10

Sex discrimination at Berkeley

• The University of Berkeley some years back (1973) found evidence
that there was sex discrimination in admission to graduate school.

• It was observed that
(1) A smaller percentage of women were admitted to graduate school than men.

• But when the University looked more closely at the evidence, they
also found that:

(2) In each department, the percentage of women admitted is the same as the percentage
of men.

• How can (1) and (2) both be true?

• The answer is that this is an instance of Simpson’s paradox. But what
does that mean?

Actual lawsuit

Slide 11

Simpson’s paradox

Applicants Admitted

Men 8442 44%

Women 4321 35%

Men Women

Major Applicants Admitted Applicants Admitted

A 825 62% 108 82%

B 560 63% 25 68%

C 325 37% 593 34%

D 417 33% 375 35%

E 191 28% 393 24%

F 272 6% 341 7%

Kano

Slide 13

Why design a survey

• It is difficult to use surveys

• Without a design there is a high probability of obtaining misleading information

• Things that go wrong with surveys:
• The questions are not clear

• The respondent loses interest

• The results are in a form that is difficult to analyse

• Sample does not represent population

• Respondents do not represent the sample

Satisfaction as a function of need fulfilment

Slide 14

(Broken Process)
(Product Failure)

Dissatisfied
Feeling

Satisfied
Feeling

C
u

st
o

m
e

r
S

a
ti

sf
a

ct
io

n

Fulfilment Fulfilled
Condition

Unfulfilled
Condition

(Perfect Process)
(Product Performs)

y-axis is Customer
Satisfaction

x-axis is the degree to
which the desired service

or product is fulfilled

Three dimensions of customer needs

Slide 15

(Broken Process)
(Product Failure)

Dissatisfied
Feeling

Satisfied
Feeling

C
u

st
o

m
e

r
S

a
ti

sf
a

ct
io

n

Fulfilment Fulfilled
Condition

Unfulfilled
Condition

(Perfect Process)
(Product Performs)

Delighters

One-Dimensional

Must-Be
Basic Function

Slide 16

Kano questionnaire definitions

• Requirement type
• Must-be

• One-Dimensional

• Delighters

• Indifferent

• Reverse, Questionable

• Definition
• If the product does not have this no one will

be interested in it.

• The more you provide this function the more
satisfied the customer will be.

• The customer is happy when it is there but
will not complain if it is not there.

• The customer does not care about this
feature.

• Poor question wording, or under certain
circumstances, this particular function has a
negative interaction with other important
functions and we never really understood
what we were talking about.

Slide 17

Questionnaire development
• Develop a pair of questions for each potential

requirement.

• Two part questions

• How do you feel if the feature (or function) is present in the
product/service?

• How do you feel if the feature (or function) is NOT present in
the product/service?

• Multiple choice answer
1. I like it that way
2. It must be that way
3. I am neutral
4. I can live with it that way
5. I dislike it that way

Functional

Dysfunctional

Kano questionnaire example

How do you feel if your radio has

Bluetooth?

1. I like it that way

2. It must be that way

3. I am neutral

4. I can live with it that way

5. I dislike it that way

How do you feel if your radio

does not have Bluetooth?

1. I like it that way

2. It must be that way

3. I am neutral

4. I can live with it that way

5. I dislike it that way

Dysfunctional form of the
Question

Functional form of the
Question

Slide 19

Legend
D: Delighter I : Indifferent
M: Must-be R: Reverse
O: One-dimensional Q: Questionable result

Customer Dysfunctional
Requirements 1. Like 2. Must-Be 3. Neutral 4. Live With 5. Dislike

Functional Q D D D O
R I I I M
R I I I M
R I I I M

1. Like
2. Must-Be
3. Neutral
4. Live With
5. Dislike R R R R Q

Kano evaluation table

Slide 20

Kano evaluation table example

1. Collect and tally each of the paired customer responses into appropriate location
in Evaluation Table.

2. Highest number wins.

3. Ties normally indicate that additional information is required. You may be dealing
with 2 market segments, or you may need to ask questions about more detailed
customer requirements.

4. Large number of Q’s indicates that questions should be temporarily deleted until
confusion can be resolved.

5. Large number of R’s indicates marketplace thoughts are opposite of the creators.

Question M O D I R Q Total Grade
1 1 21 1 23 O
2 22 1 23 M
3 5 13 5 23 D
4 1 4 6 11 1 23 I
5 9 6 1 6 1 23 M
6 2 7 10 3 1 23 I

Slide 21

Graphical approach

1. Calculate Dissatisfaction and Satisfaction Indices:

2. Plot DI vs. SI (Kano diagram)




+++

+
−=

IDOM

OM
DI

IDOM

OD
SI

+++

+
=

Delighters gone wrong

• The Cadillac Fleetwood V8-6-4
• Cylinder deactivation to keep up with the CAFE standards

• Jerky ride

• Stalled often

• Toyota Auto Park

Slide 22

Slide 23

Web based survey case study

• US Automotive consumers given J.D. Power customer satisfaction survey

• Survey has large impact on vehicle sales

• Survey has no value for diagnosing problems and improving

• Question type

• How satisfied are you with your radio?

• How satisfied are you with your seats?

• Why don’t you like the radio?

• What can I change to make you like it?

Slide 24

Customer satisfaction survey

• 181,000 July and August 2000 buyers & lessees were requested to participate
at 3-4 months service

• 80 Vehicle lines included in survey

• 10,758 Surveys were completed

Slide 25

Customer satisfaction survey

• How satisfied are you with your radio?
• Satisfaction scale is 1 to 7

• If user answers 1, 2 or 3 they are given drill down questions
• Select one or more of the following radio problems

• Reception

• Volume

• Clarity

• Controls

• Etc.

• Drill down continues

• Open ended comments are allowed

• With no incentives the average response time was 45 minutes

Customer satisfaction survey
Customer Insight Diagnostic Survey
• #1 Instrument Panel complaint was customer wants an ashtray &

• lighter

• Make & Model and sample comments specifically related to not

• including ashtray & lighter as standard feature

• – Honda Civic (x8) “It costs extra for an ashtray and a cigarette lighter. I think that’s ridiculous”

• – Saturn SL2 (x2) “There is no ashtray or any receptacle for small trash items such as gum wrappers”

• – Toyota Avalon “Centre console needs wire slot for power plug to close lid”

• – Saturn SC“No ashtray or lighter”

• – Mercury Mystique “No ashtray”

• – Mazda 626 (x2) “Did not come standard with ashtray”

• – Honda Accord “No ashtrays”

• – Pontiac Bonneville “Need a car phone jack”

• – Cadillac Seville (x3) “Front ashtray/lighter not standard but should be in this class of car”

• – Mercury Villager “No ashtray”

• – Chrysler T&C “What ashtray”

• – Honda CRV “No cigarette lighter!”

Slide 26

Slide 27

Summary

• Planning and design of the survey is important to obtain meaningful results.

• Sample selection must ensure the population is adequately represented.

• Wording and order of questions and answer choices should be thought out to
increase response rate and accuracy.

• The analysis strategy must be considered upfront in the survey design.

• If the survey is designed well, conducting the survey and analysing the results
will be easy.

Triz & 6-3-5

TRIZ

• Theory of inventive problem solving

• Creativity by resolving conflicts

• Based on patent review

• www.TRIZ40.com

Slide 29

Brainwriting 6-3-5

• Provides a basic worksheet for team members to record their ideas.

• Leverages synergies between team members to develop the ideas that feed off of
each other.

• Worksheet helps to ensure repeatable results.

• Process:
• Assembly a team (six is an ideal number) and state the problem statement
• Have each of the six people write down (3) ideas on their individual worksheet within a five

minute time frame
• Write each idea as concise but in a complete sentence (one idea per box)

• At the end of the five minutes, everyone passes their individual worksheet to the person on
their left

• The next person reads the ideas written by the person before them and then is given five
more minutes to think of another (3) ideas – these new ideas can be spurred on by the
previous ideas list

• The process is repeated until each of the six people contribute to each sheet

Slide 30

Brainwriting 6-3-5

Problem Statement:

Person Idea 1 Idea 2 Idea 3

1

2

3

4

5

6

Pugh’s Concept Selection

Pugh’s method

• Creativity – a final opportunity to be creative
• Structured method to evaluate multiple alternatives in the concept development phase

• Capture best elements of concepts to synthesise better concepts

• Proactive team approach that creates change improvements in development versus
implementation process

• Increase team’s understanding of design capability

• Optimise development time and costs

Team participants using this process often:
• To achieve greater insight and awareness of possible solutions by

building on each others ideas
• To find that the method stimulates generation of new and better

concepts

Slide 33

Pugh’s concept selection: Process flow

Slide 34

Rate concept alternatives

Create hybrid concepts

Select reference concept

Create concept screening matrix

Reflection

time

Concept Selection

Number of Concepts

Choose criteria

• List requirements against which the concepts will be evaluated

• Final list should be unambiguous and must be agreed by the full team

• Target number of criteria is about 10. If you have more, focus on most important
requirements

• Ideally, use the functional and attribute requirements from QFD HOQ #1

Slide 35

Requirements Datum 1 2 3 4

Total +
Total –
Total S’s

Concepts

QFD
HoQ#1

Functional & Attribute

Characteristics (HOW’s)

Form screening matrix

Slide 36

Problems
(requirements)
on left vertical
axis

Concepts across the top horizontal

A + – + +

B + – + +

C – + – –

Tips:

A. Team discusses criteria (requirements or metrics) — “will

they distinguish one concept for another?”

B. Attach individual solution concepts across the top.

Example: Pugh concepts for car horn

Slide 37

Example: Pugh matrix for car horn

Slide 38

Statistics homework help

As a healthcare professional, you will work to improve and maintain the health of individuals, families, and communities in various settings. Basic statistical analysis can be used to gain an understanding of current problems. Understanding the current situation is the first step in discovering where an opportunity for improvement exists. This project will assist you in applying basic statistical principles to a fictional scenario in order to impact the health and wellbeing of the clients being served.

You are currently working at Grady Memorial Hospital in the Infectious Diseases Unit. Over the past few days, you have noticed an increase in patients admitted with a particular infectious disease. You believe that the ages of these patients play a critical role in the method used to treat the patients. You decide to speak to your manager and together you work to use statistical analysis to look more closely at the ages of these patients. You do some research and put together a spreadsheet of the data that contains the following information:

· Client number

· Infection Disease Status

· Age of the patient

You need the preliminary findings immediately so that you can start treating these patients. So let’s get to work!!!!

The data set consists of 60 patients that have the infectious disease with ages ranging from 35 years of age to 76 years of age for Grady Memorial Hospital.

Statistics homework help

QUALITATIVE RESEARCH PAPER 1

Sample of the Qualitative Research Paper

In the following pages you will find a sample of the full BGS research qualitative paper

with each section or chapter as it might look in a completed research paper beginning with the

title page and working through each chapter and section of the research paper.

QUALITATIVE RESEARCH PAPER 46

Full Title of the Paper

Your Full Name (as it appears on your transcript)

Trinity Washington University

I have adhered to University policy regarding academic honesty in completing

this assignment

Submitted to *Instructor Title and Name on behalf of the faculty of the School of

Business and Graduate Studies in partial fulfillment of the degree requirements

for the Full Name of the *Degree Program

Semester Year

*Use the title Dr., or Prof. if the instructor does not have an earned doctorate. Do

not use Mr. or Ms. ** For example, Master of Arts in Communication, Master of

Science Administration in Federal Programs Management.

QUALITATIVE RESEARCH PAPER 45

Abstract

The abstract consists of 150 to 250 words in a single paragraph, see APA 6
th

Publication Manual

section 2.04 for guidelines regarding items to be included. After the abstract one the same page

and starting a new paragraph are keywords, in italics, that will assist others in researching

scholarly work related to your topic. Remember there is no indent in this paragraph. Your

instructor may determine the length of the abstract as long as it fits the parameters of no more

than 250 words. The abstract should be comprised of the following sentences:

One to two sentence(s) covering the general context of the research topic

One to two sentence(s) regarding the specific research problem

One sentence regarding the research methodology

One to two sentences regarding the significant findings

Some instructors will require a sentence regarding the conclusions and recommendations

Keywords: Include topic, major theories, keywords others might use to find your work, research

methods.

*Note that the shortened title header and page number begin here on the second

page with page # 2. When you set up your shortened title as the header, do that

on the title page, then select different first page in the header design tab. Also,

there should be no lists in an abstract. It is one solid paragraph, two if necessary.

*Acknowledgements or Dedications would each have their own page following

the abstract. *All front matter has regular, not bold, headings and the front matter

does not appear in the table of contents.

QUALITATIVE RESEARCH PAPER 45

Table of Contents

Page

Introduction ……………………………………………………………………………………………………………….. 6

Statement of the Problem …………………………………………………………………………………….6

Purpose of the Study …………………………………………………………………………………………..6

Significance of the Study …………………………………………………………………………………….7

Theory or Theoretical Perspective ………………………………………………………………………..7

Research Method ……………………………………………………………………………………………….7

Definition of Key Terms ……………………………………………………………………………………..8

Delimitations …………………………………………………………………………………………………….8

Limitations of the Study ……………………………………………………………………………………..8

Summary ………………………………………………………………………………………………………….9

Literature Review………………………………………………………………………………………………………. 10

Sections …………………………………………………………………………………………………………. 10

*Subject of Case Study …………………………………………………………………………………….. 10

Review of Related Research ……………………………………………………………………………… 11

Theoretical Construct ………………………………………………………………………………………. 11

Summary ……………………………………………………………………………………………………….. 13

Research Methodology ……………………………………………………………………………………………….. 14

Research Questions …………………………………………………………………………………………. 16

Setting …………………………………………………………………………………………………………… 18

Population ……………………………………………………………………………………………………… 18

*Data Source(s) ………………………………………………………………………………………………. 19

Ethical Considerations ……………………………………………………………………………………… 19

Research Design ……………………………………………………………………………………………… 20

QUALITATIVE RESEARCH PAPER 45

*Intervention Protocol ……………………………………………………………………………………… 21

Interview Instrument and Protocol ……………………………………………………………………… 21

Data Analysis Strategy …………………………………………………………………………………….. 22

Summary ……………………………………………………………………………………………………….. 23

Findings …………………………………………………………………………………………………………………… 24

Participants …………………………………………………………………………………………………….. 24

Data Analysis Strategy …………………………………………………………………………………….. 25

Data Analysis and Coding ………………………………………………………………………………… 27

Summary ……………………………………………………………………………………………………….. 31

Discussion………………………………………………………………………………………………………………… 32

Research Questions …………………………………………………………………………………………. 33

Conclusions ……………………………………………………………………………………………………. 34

Recommendations and Implications for Theory, Research, and Practice …………………… 35

Summary ……………………………………………………………………………………………………….. 36

References ……………………………………………………………………………………………………………….. 37

Appendices ………………………………………………………………………………………………………………. 38

Appendix A: Recruitment Materials: English ……………………………………………………….. 39

Appendix B: Recruitment Materials: Español ………………………………………………………. 41

Appendix C: Informed Consent Form …………………………………………………………………. 43

Appendix D: Survey Instrument …………………………………………………………………………..1

*Use Heading One, primary level heading, for each chapter, and Heading Two for

each secondary level heading (indented 0.5”) for each section within the chapter.

Third level and below headings do not appear in the Table of Contents. The Table

of Contents ends with the Appendices section. Use the MS Word heading

function to establish your two heading levels and to edit how they appear in the

QUALITATIVE RESEARCH PAPER 45

document. Then you can use the Table of Contents builder to auto-create the

table of Contents. Microsoft Help in MS Word can assist you with learning this.

List of Tables

Page

Table 1. Meta-codes: The three aspects of Latina women’s culture ……………………………………. 30

List of Figures

Page

Figure 1. The quantitative theoretical framework ……………………………………………………………. 13

*Note: you may place the list of tables and the list of figures on one page, but you

should choose to put them on separate pages if either list is extensive.

QUALITATIVE RESEARCH PAPER 45

Introduction

The introduction is developed in a preamble section that is not labeled as a subsect ion.

The introduction is developed in one to two paragraphs discussing the general context of your

research topic. You may recognize this as your background to the study. This is both an

expansion of your abstract and a more concise summation of your Literature Review. This will

determine the outline of the body of the Literature Review. Think of this as an outline or a

thumbnail sketch of the highlights of your Literature Review. Since it is a summation of other

author and theorists work remember to cite heavily at the end of the paragraphs or as needed in

the text. You should plan on one to two paragraphs of general context regarding your research

topic, which you might consider a state of world affairs briefing, at least the nation of your

research topic. Then provide one to two paragraphs of more specific context regarding your

topic, this might be considered the state of your community briefing. You are preparing your

audience to understand and accept the statement of the problem.

For example, you might discuss in the general context the history of synthetic marijuana

use. Then in the specific context you might discuss the upsurge in synthetic marijuana use.

Statement of the Problem

You will provide one concise paragraph discussing your research problem. Be specific in

describing this problem. For example, you might discuss the problem of the recent increase in

synthetic marijuana use among preteens in Northwest DC and the resulting risks to their health

and lifestyle. Remember you have prepared the reader with the preamble above this section.

Purpose of the Study

Discuss in one paragraph what you will do in the research. This is made obvious in the

argument of the Literature Review. This is a brief statement of how you will investigate the

QUALITATIVE RESEARCH PAPER 45

research problem. For example, the purpose of this study is to examine the prevalence of the use

of synthetic marijuana use among preteens which will lead to a prevention and intervention

model to be used in community centers citywide.

Significance of the Study

Discuss what the benefit will be of addressing the research problem might be to the

population of your study, the academic community. For example, Health professionals,

educators, staff members, and concerned citizens will have relevant information and an

intervention model they might make use of to curb preteen use of synthetic marijuana.

Theory or Theoretical Perspective

A brief discussion of the theory your quantitative research study is investigating, or a

brief discussion of the theoretical perspective of your qualitative research. You might have a

specific rationalist or modernist theory that describes cause and effect and you would discuss that

theory. Or you might perceive this problem to be a result of a social construction in the

discourse between parents and children and you would discuss social constructionism, or the

conversations in society concerning the benefits of rebellious individualism. So you would

discuss the theories of hegemonic language and the process of de-centering the discourse to

change the source of power in the discourse. In another example, you might compare the five

common health behavioral models to the results of the study and suggest my own intervention

model. So you would discuss the overarching theoretical field of behavioral change.

Research Method

A concise paragraph describing the research method used to investigate the problem.

This can later be expanded into the preamble of your research methods chapter. Cite the

textbooks and research articles, which inform you. Creswell’s Research Design, 3
rd

or 4
th
ed.

QUALITATIVE RESEARCH PAPER 45

Have great discussions of quantitative research methods and useful checklists. Additionally,

language from Merriam’s, Qualitative Research, can be helpful.

Definition of Key Terms

Keep this brief, if extensive a glossary is required, which would belong in the appendices

Each definition appears as a third level heading in this section. Cite the sources of your

materials. For example:

De-centering: a means of changing the power of negative or oppressive words and

phrases that hegemonic cultures subconsciously use to impose and maintain the power

relationships in the cultures as defined and proposed by Jacques Derrida (Hatch & Cunliffe,

2006, p. 311).

And so on…

Delimitations

Most research topics cover areas that are far too multitudinous, multifaceted, complex, or

inexhaustible to be addressed in a research study of any scope, say nothing of an undergraduate

or a graduate level research paper. There are research directions and research questions

suggested by your research topic but are not addressed in this research study. Discuss a few of

these to show that you know where your research fits in its scholarly community and that you

know what you can accomplish

Limitations of the Study

Describe what your research design cannot accomplish due to the scope of the project,

limitations of time and resources. However, do not adopt a whiny and petulant tone; you are

simply acknowledging reality, as does every other student in your position. For example, Due to

the scope of this research project you are not able to collect data from the entire recommended

QUALITATIVE RESEARCH PAPER 45

population sample, so your study is limited by the number of participants, or that you used a

convenience sample.

Summary

Then the author would wrap up the chapter with the summarization of the chapter and a

transition to the next chapter as described above. Notice that this section started with a

secondary level heading. Each section within a chapter uses a second level heading, which

appears in the table of contents, indented and below the chapter heading.

QUALITATIVE RESEARCH PAPER 45

Literature Review

The literature review begins with a Preamble, which is not indicated with a heading.

This is presented differently from the introduction chapter. In two to four paragraphs discuss set

the context for your literature review and discuss what you will cover or accomplish in this

chapter.

Sections

One each as determined by the theoretical construct or theoretical framework and as

many as necessary to support the academic argument and exhibit inclusion of the scholarly

community(ies) and the student’s competence and mastery of the subject. Do not forget current,

previous research, and alternate research methods used to investigate your research topic.

Additionally be certain to include critiques of the works you cover in this chapter. These

develop the reader’s understanding of the context of the research problem and lead to the

discovery of the theoretical construct or theoretical framework, the research problem and the

research questions. The literature review shows the unique approach of the study and how it

adds to the body of knowledge and informs the scholarly or practitioner communities and

includes the theories that will inform the research study

*Subject of Case Study

This is an alternate section that applies only to case study research. Students pursuing a

case study will present an additional section for the subject of their case study. This section will

be titled for the case study. This is a thorough discussion of the subject and not and exposition of

the data you will discuss in the findings chapter. If you are pursuing a study with multiple cases

you will present a section for each case subject.

QUALITATIVE RESEARCH PAPER 45

Review of Related Research

Review the methods others have used to explore topics similar to yours and discuss how

they inform your perspective and your research project.

Theoretical Construct

In the qualitative research project this is the Theoretical Construct and would include the

theory which is the based on the theoretical perspective and the factors or subjects which relate,

or bound, the theory to the research problem. This is your working theory of the phenomena

under investigation.

You will describe your theoretical construct as a model of your research problem. This is

the precise meaning (working definition) the factors will have in your study and not the broader

meanings that might be apparent in the literature review. You will also develop a visual

representation (figure) of your model and present it here in the paper. This is your opportunity to

show your competence and your mastery of the literature ante the problem. You might have

instructors who ask that the theoretical construct appear in a separate chapter at their prerogative.

Please comply with your grading instructor’s request.

Name and define the phenomenon or the outcome state and provide a brief description of

each, much like your definition of key terms. This clarifies for the reader the specific nature of

your variables and limits their interpretation by critics. Then provide the figure that models your

theoretical construct.

Factor one. Use the name of this factor for the title of this heading, and provide a brief

and concise paragraph of description. This is the working definition of this factor in your study,

other definitions or uses will not apply to your study. Use citations to support this working

definition. And so on for each factor which comprises the theoretical construct. These should

QUALITATIVE RESEARCH PAPER 45

not come as a surprise to your reader since they build on or are reduced from information in your

literature review.

Factor 2. and etcetera.

Figure 1. Qualitative theoretical construct as a literature map. (Mattern as cited in, Creswell,

2009, p.35). A map such as this shows the relationship between the factors (commerce and

information management) and their subfactors on Research in Managing IT in New Zealand and

that research’s resulting factors.

QUALITATIVE RESEARCH PAPER 45

Figure 2. Qualitative theoretical construct as a process

Figure 3. Qualitative theoretical construct as a cycle

Summary

And of course, end your chapter with a brief discussion of what you have covered in this

chapter and transition to the next chapter.

Effects of environment on
childhood obseity

Nutriononal
choices

Food
Options

Poverty

Academic
rigor

Physical
Stress

Psychological
Sress

Complex
assignment

Vague
direction

Precedents
for

Plagiarism

QUALITATIVE RESEARCH PAPER 45

Research Methodology

The research methodology section describes the worldview or philosophy, the

underpinning practices and procedures for conducting and replicating your research, and the type

or research study this is (observation, field, natural, or quasi- experiment). It also informs

scholars and practitioners regarding the rigor and the appropriateness of your methodology in

relation to the scholarly community in which the research belo ngs. Some research

methodologies are rigid in their expectations and do not allow for variance, while others allow

for variation in the form of the research design, which can make each research project unique.

This is acceptable as long as the research design is approved by your faculty and can be

replicated. Please do not over invest your time until your instructor has approved your research

methodology. Cite the textbooks and research articles, which inform you. Creswell’s Research

Design, 3
rd

or 4
th
ed. Have great discussions of qualitative research methods and useful

checklists. Additionally, language from Merriam’s, Qualitative Research, and Remler and Van

Ryzin’s, Research Methods, can be helpful.

*Institutional Review Board (IRB) and Ethical Conduct in Research.

This section also provides important information used for preparing the

Institutional Review Board (IRB) approval request. As you know by now the IRB

must approve your research prior to interacting with human subjects or collecting

data from human subjects. It is recommended that studies that do not intend to

interact with human subjects apply and receive approval from the IRB to prevent

unintended harm to others and the loss of the resulting research data. Please be

certain to use the BGS specific IRB forms and procedures.

All research regardless of whether or not it interacts with humans must

apply to and be approved by the IRB. All research involving human interaction

must include a signed informed consent form. Subjects under the age of eighteen

and others who are not able to sign for themselves are not included in BGS

QUALITATIVE RESEARCH PAPER 45

student research. You will need to keep the consent forms and information

confidential and separate from the data. Confidentiality means that you may not

reveal who participated in your research, unless otherwise directed by an agent of

the university, which should come through the IRB, the Dean’s Office, or your

instructor. Your instructor or the IRB can ask to review your consent

documentation to verify the authenticity of your participants.

A common pitfall for students is that they test their data collection

instruments with likely subjects or begin to collect data PRIOR to receiving

approval to their research by the IRB. These students must destroy this data and it

cannot be used in the research study. Violation of this policy might lead to an

academic dishonesty hearing and the potential for being dismissed from the

university.

Students will find examples of suggested sections to include in several

types of research methodology. You might find that you need additional sections

to adequately discuss and describe your research methodology. Chose the

appropriate format in conjunction with your instructor, who may suggest

alternative sections and formats as are appropriate to your research methodology.

Remember, the instructor has the final say regarding these sections. The option

presented below is for a quantitative research project or study, with human

interaction or with archived data. The title of this section would not be included

in your paper, it is provided as a marker of the beginning of a new section. The

preamble would follow directly after the chapter heading: Research Methodology.

Begin the chapter with a preamble (a discussion of what will be covered or accomplished

in this chapter and is presented without a subsection heading). Here you might address the

worldview or philosophy that guides your research and provide a general discussion of your

methodology. Your research methodology is essentially concerned with your strategy for

collecting data and informing your readers of how you will ensure the replicability and rigor of

your strategy. Your research design might vary depending on whether or not you intend to

introduce an intervention and measure its results. Intervention research studies would then

QUALITATIVE RESEARCH PAPER 45

include both the plan for the intervention and the instrument you will use to measure the effects

of the intervention. Research studies that plan to measure and explain an existing phenomenon

without an intervention would include the data collection instrument. Think of this as the warm

up for the full discussion of your data collection strategy in the sections below.

*Please note that it is important to distinguish and understand prior to

your Research Design (or Research Strategy) section there is a difference between

studies involving human intervention and those that rely on secondary forms of

data. To start a human intervention study, after the preamble you would begin

with the sections: Setting, and Population. Studies using secondary data you

would start with Data Source (or Sources) after the preamble and then move to the

Research Design section. A study involving both human participants and

secondary data you would use all three sections. All three of these sections are

described below. Use the ones appropriate to your study.

Research Questions

List and then discuss each of the general questions that determine what methods you will

use and what type of data you will collect. These are indicated by the research problem and

bound by your theoretical perspective and your research methodology. These are later made

obvious in the argument of the Literature Review. For example,

Example one:

The researcher sets out to examine the decision-making styles and the effects it has on

employee performance in the workplace. Research was conducted by a content analysis utilizing

the results of searching numerous scholarly journals that have conducted research on decision-

making styles in the workplace and how leaders arrive at making the decisions they make in the

workplace.

QUALITATIVE RESEARCH PAPER 45

Research question one (RQ1): How might leader’s decision-making styles effect em-

ployee performance?

Proposition one (P1): Leader’s decision-making styles are informed by emotions or feel-

ings.

Leader’s decision-making styles may effect employee performance by making decisions that are

not popular with the employees. Boachie-Mensah, Dogbe, and Ophelia (2011). The main

objective of this study was to assess the impact of performance-related pay on the motivation of

employees and subsequently, on the achievement of organizational goals. Pay increases or the

lack of for employees can have an effect on employee’s and the productivity of their work. If the

employee feels they aren’t being compensated for their work they may tend to decrease in being

productive in their work.

Example two:

With numerous organizations as well as government agencies awarding several grants

with the intention of narrowing the achievement gap, how well is that impact.

Research question one (RQ1). What is the impact of additional funding on the achieve-

ment gap?

Research question two (RQ2). Are there increased numbers of minority students scoring

at higher percentages than previously?

It is an anticipated outcome that a model will be created to determine which areas are

more in need of this level of funding, which have been successful through the lenses of

educators. What it took to achieve this level of success in those programs and how they were

funded previously will help develop a model of the actual implementations needed to narrow the

gap.

QUALITATIVE RESEARCH PAPER 45

Setting

For studies involving human participants discuss where you will find your potential

research participants. For example if you are conducting an observation in the courtyard of the

Reagan building you would describe that location and environment in detail, and why it is

appropriate to finding the population.. If you are recruiting from a specific government agency

you would describe it briefly and then give detail about why it is an appropriate setting for

recruiting your population.

Potential participants will be found using the Internet as a search tool. Links to the

electronic interview will be emailed to the researcher’s personal contacts as well as posted on

Facebook and LinkedIn venues. In-person interviews will be conducted and recorded in a quiet,

neutral location where the participants are not in danger and there is no intimidation or coercion.

Population

For studies involving human participants calculate and then discuss the suggested

demographics and the sample size of the population. Be sure to support your population choice

and then the type of sampling y

Statistics homework help

Week 1 Assignment


Adapted from Statistical Reasoning for Everyday Life (Bennett, Briggs, & Triola, 2017).

Understanding:

• Define the terms as they apply to statistical studies: sample, raw data, sample statistic, confidence interval, margin of error, census.

• Describe the five basic steps in a statistical study. Give an example of their application for a topic related to your research interests.

• Explain why the following statement is true: The 95% confidence interval for a poll suggested that support for Governor Garcia is between 55% and 60%. Therefore, we can be certain that a majority of the population supports the governor.

• Explain why this is false: One study of heart disease involved treating male physicians with daily doses of aspirin. Because the study concluded that aspirin helps males avoid heart disease, it follows that females can also avoid heart disease by taking aspirin.

• What is peer review, and why is it useful?

Application:

• In a Harris Interactive survey of 1006 adults, 86% say that they wash their hands after using a public restroom; the margin of error is 3 percentage points. USA Today reported that among 6028 adults observed in restrooms, 85% washed their hands; the margin of error is 1 percentage point. Use the given statistics and margin of error to identify the confidence interval for each study. Which study do you believe, and why?

• In a survey of 1002 people, 701 (70%) said that they voted in the last presidential election (based on data from ICR Research Group). The margin of error for this survey was 3 percentage points. However, actual voting records show that only 61% of eligible voters cast a vote. Does this imply that people lied when responding to the survey? Explain.

• Describe how you would apply the five basic steps in a statistical study to the following research question: determine the percentage of drivers who text while they are driving.

• The Journal of American Psychologists prints an article evaluating a new drug for depression. The researchers who wrote the article received funding for their labs from the pharmaceutical company that produces the drug. Is there a potential for bias in this research study? How could it be avoided? Explain your answer.

• A college dean obtains an alphabetical list of all full-time students at her college and selects every 50th name on that list to survey those students regarding the total amount of student loan debt that they will have upon graduating. She then reports this average (mean) amount of debt among these students as the average of all college students. What type of sample of this? What could she do to improve her sample?

• Explain any problems likely to cause confounding, and suggest how they could be avoided: in a comparison of gasoline with different octane ratings, 24 vans are driven with 87 octane gasoline, and 28 SUVs are driven with 91 octane gasoline. After each vehicle has been driven for 250 miles, the amount of gasoline consumed is measured.

• Explain which of the 8 guidelines for evaluating a statistical study might be most relevant: In a survey of 1,200 college students, each was asked whether they are a good person.

• The following presents a headline in a local newspaper, as well as the story summary. Discuss whether the headline accurately represents the story.

Headline: “Drugs Shown in 98% of Movies”

Story Summary: A “government study” claims that drug use, drinking, or smoking was depicted in 98% of top movie rentals (Associated Press).

• What crucial information is missing from the following “sound bite”? A USA Today “Snapshot” reported that the percentage of people with diabetes who don’t know that they have diabetes is “1 in 4.” The source was given as the American Diabetes Association.

• What crucial information is missing from the following “sound bite”? CNN reports on a Zagat survey of America’s top restaurants, which fund that “only 9 restaurants achieved a rare 29 out of a possible 30 rating, and none of these restaurants are in the Big Apple.”

Statistics homework help

Chapter 4

Summarizing Data Collected in the Sample

Learning Objectives (1 of 3)

Distinguish between dichotomous, ordinal, categorical, and continuous variables

Identify appropriate numerical and graphical summaries for each variable type

Compute a mean, median, standard deviation, quartiles and range for a continuous variable

Learning Objectives (2 of 3)

Construct a frequency distribution table for dichotomous, categorical, and ordinal variables

Provide an example of when the mean is a better measure of location than the median

Interpret the standard deviation of a continuous variable

Learning Objectives (3 of 3)

Generate and interpret a box plot for a continuous variable

Produce and interpret side-by-side box plots

Differentiate between a histogram and a bar chart

Variable Types

Dichotomous variables have two possible responses (e.g., yes/no).

Ordinal and categorical variables have more than two responses, and responses are ordered and unordered, respectively.

Continuous (or measurement) variables assume in theory any values between a theoretical minimum and maximum.

Biostatistics

Two areas of applied biostatistics

Descriptive statistics—summarize a sample selected from a population

Inferential statistics—make inferences about population parameters based on sample statistics.

Vocabulary

Data elements/data points

Subjects/units of measurement

Population versus sample

Sample vs. Population

Any summary measure computed on a sample is a statistic.

Any summary measure computed on a population is a parameter.

n = Sample Size

N = Population Size

Example 4.1.
Dichotomous Variable

Frequency Distribution Table

Relative Frequency Bar Chart for Dichotomous Variable

Sample: n = 50

Population: Patients at health center

Variable: Marital status

Marital Status Number of Patients
Married 24
Separated 5
Divorced 8
Widowed 2
Never married 11
Total 50

Categorical Outcome (1 of 2)

Categorical Outcome (2 of 2)

Frequency Distribution Table

Marital Status Number of
Patients (f)
Relative Frequency
(f/n)
Married 24 0.48
Separated 5 0.10
Divorced 8 0.16
Widowed 2 0.04
Never married 11 0.22
Total 50 1.00

Frequency Bar Chart

Sample: n =50

Population: Patients at health center

Variable: Self-reported current health status

Health Status Number of Patients
Excellent 19
Very good 12
Good 9
Fair 6
Poor 4
Total 50

Ordinal Outcome (1 of 2)

Ordinal Outcome (2 of 2)

Frequency Distribution Table

Heath Status Freq. Rel. Freq. Cumulative Freq. Cumulative Rel. Freq.
Excellent 19 38% 19 38%
Very good 12 24% 31 62%
Good 9 18% 40 80%
Fair 6 12% 46 92%
Poor 4 8% 50 100%
50 100%

Relative Frequency Histogram

Poor Fair Good Very Good Excellent 8 12 18 24 38

Health Status

%

Example 4.2.
Ordinal Variable

Frequency Distribution Table

Relative Frequency Histogram
for Ordinal Variable

Assume, in theory, any value between a theoretical minimum and maximum

Quantitative, measurement variables

Continuous Variable (1 of 9)

Population: Patients 50 years of age with coronary artery disease

Sample: n = 7 patients

Outcome: Systolic blood pressure (mmHg)

Continuous Variable (2 of 9)

Sample data

X 100 110 114 121 130

130 160

Continuous Variable (3 of 9)

X 100 110 114 121 130

130 160

865

Continuous Variable (4 of 9)

Consider a second sample from the same population.

We record SBP on each subject in the second sample:

120 121 122 124 125 126 127

n = 7

= 865 / 7 = 123.6.

What is different between the two samples?

Continuous Variable (5 of 9)

23

Dispersion

X (X – )
100 –23.6
110 –13.6
114 –9.6
121 –2.6
130 6.4
130 6.4
160 36.4
865 0

Continuous Variable (6 of 9)

Dispersion

X (X – )
100 –23.6
110 –13.6
114 –9.6
121 –2.6
130 6.4
130 6.4
160 36.4
865 0

Mean absolute

deviation (MAD):

Continuous Variable (7 of 9)

Sample variance

X (X – ) (X – )2

100 –23.6 556.96

110 –13.6 184.96

114 –9.6 92.16

121 –2.6 6.76

130 6.4 40.96

130 6.4 40.96

160 36.4 1324.96

865 0 2247.72

Continuous Variable (8 of 9)

Continuous Variable (9 of 9)

Sample standard deviation

Standard summary

n = 7, X = 123.6, s = 19.4

Median

Median

100 110 114 121 130 130 160

Median—holds 50% of values above and 50% of values below

Order data

For n odd—median is middle value

For n even—median is mean of two middle values

Quartiles

Q1 = first quartile holds approximately 25% of the scores at or below it.

Q3 = third quartile holds approximately 25% of the scores at or above it.

Q2 = ??

Continuous Variable

Median

Order data

100 110 114 121 130 130 160

Q1

Q3

Box and Whisker Plot

100 110 120 130 140 150 160

Min Q1 Median Q3 Max

Comparing Samples with
Box and Whisker Plots

100 110 120 130 140 150 160

Summarizing Location and Variability

When there are no outliers, the sample mean and standard deviation summarize location and variability.

When there are outliers, the median and interquartile range (IQR) summarize location and variability, where IQR = Q3 – Q1.

Sample: n = 51 participants in a study of cardiovascular risk factors.

Variable: age (years)

60 62 63 64 64 65 65 65 65 65 65

66 66 66 66 66 67 67 67 68 68 68

70 70 70 71 71 72 72 73 73 73 73

73 73 75 75 75 76 76 77 77 77 77

79 82 83 85 85 87

Example (1 of 2)

Example (2 of 2)

Sample mean:

Sample variance:

Sample standard deviation:

Standard summary: n = 51, X = 71.3, s = 6.4

Outliers

IQR = Interquartile Range = Q3 – Q1

= Range of middle half of the data

Outliers are values that either:

Exceed Q3 + 1.5 IQR

Fall below Q1 – 1.5 IQR

Or, are outside ± 3s

Check for Outliers in Example

Q1 = 66, Q3 = 76, IQR = 10

Lower = 66 – 1.5(10) = 51

Upper = 76 + 1.5(10) = 91

± 3s = 52.1 to 90.5

Presenting Data (1 of 2)

Suppose we collapse ages into five mutually exclusive and exhaustive categories

Age Class Number of Individuals (freq.) 60–64 5

65–69 17

70–74 12

75–79 12

80–84 2

85–89 3

Presenting Data (2 of 2)

Cumulative

Age Class Freq. Rel. Freq. Freq. Rel. Freq.

60-64 5 0.10 5 0.10

65-69 17 0.33 22 0.43

70-74 12 0.24 34 0.67

75-79 12 0.24 46 0.91

80-84 2 0.04 48 0.95

85-89 3 0.06 51 1.00

Total 51 1.00

Frequency Histogram

60-64 65-69 70-74 75-79 80-84 85-89 5 17 12 12 2 0

Age Class

Frequency

Example 4.3.
Summarizing Continuous Variables

Diastolic blood pressures in n = 10 randomly selected participants attending the seventh examination of the Framingham Offspring Study

76 64 62 81 70

72 81 63 67 77

Summarizing Location

What is a typical diastolic blood pressure?

Sample mean:

= Sum of diastolic blood pressures/n

= 713/10 = 71.3

Notation

Let X represent the outcome of interest (e.g., X = diastolic blood pressure)

Summarizing Variability

Sample range:

= maximum – minimum = 81 – 62 = 19

Sample variance:

Sample Variance (1 of 2)

DBP Deviation from Mean

76 (76 – 71.3) = 4.7

64 (64 – 71.3) = –7.3

62 (62 – 71.3) = –9.3

81 9.7

70 –1.3

72 0.7

81 9.7

63 –8.3

67 –4.3

77 5.7

S X = 71.3 S Deviations from Mean = 0

Sample Variance (2 of 2)

DBP Deviation from Mean Squared Deviations

76 (76 – 71.3) = 4.7 22.09

64 (64 – 71.3) = –7.3 53.29

62 (62 – 71.3) = –9.3 86.49

81 9.7 94.09

70 –1.3 1.69

72 0.7 0.49

81 9.7 94.09

63 –8.3 68.89

67 –4.3 18.49

77 5.7 32.49

S X = 71.3 S Deviations = 0 S Deviations2 = 472.10

Sample Variance and
Sample Standard Deviation

Median

Median holds 50% of values above and 50% of values below

Order data

For n odd—median is middle value

For n even—median is mean of two middle values

Median = 71

62 63 64 64 70 | 72 76 77 81 81

Quartiles

Q1 = first quartile holds 25% of values below it

Q3 = third quartile holds 25% of values above it

Median = 71

62 63 64 64 70 | 72 76 77 81 81

Q1 Q3

Determining Outliers

Outliers—values below Q1 – 1.5(Q3 – Q1) or above Q3 + 1.5(Q3 – Q1)

In Example 4.3: lower limit = 64 – 1.5(77 – 64) = 44.5 and upper limit = 77 + 1.5(77 – 64) = 96.5

Outliers?

Mean or median?

s or IQR?

Box Plot for Continuous Variable

Dichotomous and categorical

Frequencies and relative frequencies

Bar charts (freq. or relative freq.)

Ordinal

Frequencies, relative frequencies, cumulative frequencies, and cumulative relative frequencies

Histograms (freq. or relative freq.)

Numerical and Graphical
Summaries (1 of 2)

Numerical and Graphical
Summaries (2 of 2)

Continuous

Mean, standard deviation, minimum, maximum, range, median, quartiles, interquartile range

Box plot

Statistics homework help

Data

SubID SocialMedia DefundPolice
1 1 1
2 4 2
3 2 1
4 2 2
5 6 1
6 1 1
7 1 3
8 6 1
9 6 2
10 6 1
11 2 3
12 6 1
13 2 2
14 2 2
15 2 2
16 5 2
17 2 1
18 2 1
19 6 3
20 6 2
21 2 1
22 6 1
23 6 1
24 3 1
25 6 1
26 3 2
27 2 1
28 2 1
29 3 2
30 2 1
31 6 1
32 6 1
33 6 2
34 4 1
35 2 1
36 2 1
37 3 1
38 3 2
39 6 1
40 3 3
41 5 1
42 2 1
43 2 1
44 2 3
45 2 2
46 6 2
47 6 3
48 2 2
49 2 2
50 6 3
51 2 1
52 6 2
53 1 1
54 3 2
55 2 3
56 4 1
57 2 3
58 6 1
59 2 2
60 2 3
61 3 1
62 2 2
63 4 1
64 2 1
65 2 2
66 2 1
67 6 2
68 3 1
69 2 1
70 6 2
71 4 2
72 2 3
73 2 2
74 6 2
75 6 3
76 3 1
77 6 2
78 6 1
79 2 2
80 6 2
81 3 2
82 2 1
83 2 2
84 6 2
85 2 1
86 2 1
87 6 1
88 3 2
89 6 2
90 6 2
91 2 1
92 6 1
93 2 1
94 2 2
95 4 3
96 2 1
97 2 2
98 3 2
99 6 2
100 3 1
101 4 3
102 2 1
103 4 1
104 5 2
105 6 3
106 6 1
107 2 2
108 2 2
109 3 2
110 2 2
111 6 3
112 3 2
113 6 2
114 2 1
115 2 2
116 6 1
117 6 2
118 3 1
119 3 1
120 2 1
121 2 1
122 2 2
123 2 1
124 6 1
125 2 2
126 2 2
127 6 2
128 6 2
129 6 2
130 2 1
131 3 2
132 2 2
133 2 2
134 2 2
135 2 2
136 2 2
137 6 2
138 2 1
139 6 2
140 6 1
141 6 2
142 2 3
143 6 1
144 2 2
145 2 1
146 6 2
147 5 1
148 6 1
149 6 2
150 4 2
151 3 2
152 2 3
153 5 1
154 2 1
155 6 2
156 5 1
157 5 3
158 2 2
159 2 3
160 2 1
161 6 1
162 6 2
163 2 3
164 6 2
165 5 3
166 2 1
167 6 2
168 2 2
169 3 2
170 2 2
171 2 1
172 2 1
173 2 1
174 6 2
175 2 1
176 6 1
177 1 1
178 5 2
179 6 3
180 2 1
181 2 2
182 5 3
183 2 2
184 2 2
185 2 2
186 3 2
187 6 2
188 6 2
189 2 2
190 2 2
191 2 1
192 6 2
193 4 2
194 2 2
195 6 2
196 2 2
197 4 2
198 2 1
199 3 2
200 6 2

Codebook

Variable Description Values
SocialMedia The social media used the most (if the subject does use at least one of these platforms) 1=Facebook
2=Instagram
3=Snapchat
4=Twitter
5=YouTube
6=TikTok
DefundPolice Opinion on “Defund the Police” movement 1=Support
2=Oppose
3=Unsure

Statistics homework help

As a healthcare professional, you will work to improve and maintain the health of individuals, families, and communities in various settings. Basic statistical analysis can be used to gain an understanding of current problems. Understanding the current situation is the first step in discovering where an opportunity for improvement exists. This project will assist you in applying basic statistical principles to a fictional scenario in order to impact the health and wellbeing of the clients being served.

You are currently working at Grady Memorial Hospital in the Infectious Diseases Unit. Over the past few days, you have noticed an increase in patients admitted with a particular infectious disease. You believe that the ages of these patients play a critical role in the method used to treat the patients. You decide to speak to your manager and together you work to use statistical analysis to look more closely at the ages of these patients. You do some research and put together a spreadsheet of the data that contains the following information:

· Client number

· Infection Disease Status

· Age of the patient

You need the preliminary findings immediately so that you can start treating these patients. So let’s get to work!!!!

The data set consists of 60 patients that have the infectious disease with ages ranging from 35 years of age to 76 years of age for Grady Memorial Hospital.

Statistics homework help

ChartDataSheet_

This worksheet contains values required for MegaStat charts.
Residuals X data 3/19/2007 7:49.25
66 18 45177 34.4 31
69 16 51888 41.2 20
67 10 51379 40.3 24
70 4 66081 35.4 29
78 0 50999 31.5 18
62 28 41562 36.3 30
70 28 44196 35.1 14
84 29 50975 37.6 33
68 22 72808 34.9 28
60 42 79070 34.8 29
80 36 78497 36.2 39
64 32 41245 32.2 23
80 22 33003 30.9 22
88 78 90988 37.7 37
42 35 37950 34.3 24
68 32 45206 32.4 17
80 48 79312 32.1 37
84 32 37345 31.4 22
35 27 46226 30.4 36
84 24 70024 33.9 34
78 16 54982 35.6 26
80 39 54932 35.9 20
70 70 34097 33.6 20
76 33 46593 37.9 26
56 12 51893 40.6 21
65 32 88162 37.7 37
62 0 89016 36.4 34
66 20 114353 40.9 34
76 24 75366 35 30
92 36 48163 26.4 16
112 34 49956 37.1 28
66 15 45990 30.3 36
70 28 45723 31.3 18
60 15 43800 29.6 36
86 10 68711 32.9 18
76 0 65150 40.7 24
68 16 39329 29.3 22
64 0 63657 37.3 29
52 36 67099 39.8 25
78 26 75151 33.9 28
64 28 93876 35 40
82 32 79701 35 39
86 30 77115 35.9 30
92 16 52766 33 17
72 10 32929 30.9 22
90 24 87863 38.5 29
64 20 73752 40.5 19
80 20 85366 32.1 29
102 30 39180 34.8 18
70 26 56077 38 19
62 26 77449 37 34
68 20 56822 34.7 25
74 24 80470 36.4 30
84 14 55584 36.8 21
70 32 78001 32.2 30
96 32 75307 34.8 30
70 22 76375 36.7 28
76 32 61857 33.8 31
62 28 61312 34.2 16
92 23 72040 39 31
60 20 92414 34.9 40
54 15 92602 39.3 33
110 23 59599 35.6 28
78 0 72453 36 23
72 31 67925 41.1 16
74 29 42631 24.7 25
94 0 75652 40.5 25
80 16 39650 32.9 18
124 0 48033 30.3 15
46 20 67403 36.2 19
66 0 80597 32.4 27
63 28 60928 43.5 21
72 15 73762 41.6 29
76 24 64225 31.4 15
NormalPlot data 3/19/2007 7:49.03
-259.9497306439 -2.3669115357
-188.5900144767 -2.0061237235
-178.1863109741 -1.8007082352
-165.2888689211 -1.6514108613
-156.2930386781 -1.5318456091
-147.1995334043 -1.4308738679
-145.0204151759 -1.3426905457
-132.7962270775 -1.2638662791
-132.5838765031 -1.1921973902
-127.8657575015 -1.1261791757
-124.4916500844 -1.0647357757
-123.016384493 -1.0070695657
-118.431306853 -0.952571595
-110.8440652315 -0.9007655189
-110.1477551652 -0.8512709934
-109.3430277914 -0.8037789242
-105.1097263145 -0.7580342264
-104.7616892077 -0.7138235056
-100.1917272772 -0.6709660579
-96.9455399284 -0.6293071641
-78.5222407532 -0.588713006
-66.833182556 -0.5490667518
-63.9367962151 -0.5102654979
-54.9666697606 -0.4722178495
-49.5089341383 -0.4348419815
-43.817663257 -0.3980640685
-30.5622414309 -0.3618169976
-29.7056802184 -0.3260393031
-28.8211160258 -0.2906742745
-21.3829190469 -0.2556692022
-20.8096302471 -0.220974732
-18.0336858908 -0.1865443062
-16.4732294274 -0.152333674
-15.5268611118 -0.1183004556
-12.5832024808 -0.0844037498
-11.5991899485 -0.0506037738
-10.6416197419 -0.0168615273
-6.4663288735 0.0168615273
6.6082090726 0.0506037738
10.1026389027 0.0844037498
10.1556691582 0.1183004556
11.5424324103 0.152333674
13.4792557233 0.1865443062
15.0213966843 0.220974732
18.9663798116 0.2556692022
19.2122025279 0.2906742745
19.5938287738 0.3260393031
19.7419844304 0.3618169976
23.7470781354 0.3980640685
25.1736217387 0.4348419815
28.9194386872 0.4722178495
38.4697564504 0.5102654979
50.9831788417 0.5490667518
53.0357068283 0.588713006
61.102903906 0.6293071641
63.1204953548 0.6709660579
63.8380153718 0.7138235056
71.0833539728 0.7580342264
71.3281648375 0.8037789242
75.1828858929 0.8512709934
75.2802525469 0.9007655189
81.3206554357 0.952571595
81.6351025536 1.0070695657
105.576464442 1.0647357757
115.0253844293 1.1261791757
122.2233804168 1.1921973902
150.1178490106 1.2638662791
180.3934285167 1.3426905457
196.2671375845 1.4308738679
205.7993140008 1.5318456091
234.8563337617 1.6514108613
289.7338930992 1.8007082352
336.0904495556 2.0061237235
372.5195939607 2.3669115357
Residuals X data 3/19/2007 8:01.41
66 18 45177 34.4 31
69 16 51888 41.2 20
67 10 51379 40.3 24
70 4 66081 35.4 29
78 0 50999 31.5 18
62 28 41562 36.3 30
70 28 44196 35.1 14
84 29 50975 37.6 33
68 22 72808 34.9 28
60 42 79070 34.8 29
80 36 78497 36.2 39
64 32 41245 32.2 23
80 22 33003 30.9 22
88 78 90988 37.7 37
42 35 37950 34.3 24
68 32 45206 32.4 17
80 48 79312 32.1 37
84 32 37345 31.4 22
35 27 46226 30.4 36
84 24 70024 33.9 34
78 16 54982 35.6 26
80 39 54932 35.9 20
70 70 34097 33.6 20
76 33 46593 37.9 26
56 12 51893 40.6 21
65 32 88162 37.7 37
62 0 89016 36.4 34
66 20 114353 40.9 34
76 24 75366 35 30
92 36 48163 26.4 16
112 34 49956 37.1 28
66 15 45990 30.3 36
70 28 45723 31.3 18
60 15 43800 29.6 36
86 10 68711 32.9 18
76 0 65150 40.7 24
68 16 39329 29.3 22
64 0 63657 37.3 29
52 36 67099 39.8 25
78 26 75151 33.9 28
64 28 93876 35 40
82 32 79701 35 39
86 30 77115 35.9 30
92 16 52766 33 17
72 10 32929 30.9 22
90 24 87863 38.5 29
64 20 73752 40.5 19
80 20 85366 32.1 29
102 30 39180 34.8 18
70 26 56077 38 19
62 26 77449 37 34
68 20 56822 34.7 25
74 24 80470 36.4 30
84 14 55584 36.8 21
70 32 78001 32.2 30
96 32 75307 34.8 30
70 22 76375 36.7 28
76 32 61857 33.8 31
62 28 61312 34.2 16
92 23 72040 39 31
60 20 92414 34.9 40
54 15 92602 39.3 33
110 23 59599 35.6 28
78 0 72453 36 23
72 31 67925 41.1 16
74 29 42631 24.7 25
94 0 75652 40.5 25
80 16 39650 32.9 18
124 0 48033 30.3 15
46 20 67403 36.2 19
66 0 80597 32.4 27
63 28 60928 43.5 21
72 15 73762 41.6 29
76 24 64225 31.4 15
NormalPlot data 3/19/2007 8:01.03
-259.9497306439 -2.3669115357
-188.5900144767 -2.0061237235
-178.1863109741 -1.8007082352
-165.2888689211 -1.6514108613
-156.2930386781 -1.5318456091
-147.1995334043 -1.4308738679
-145.0204151759 -1.3426905457
-132.7962270775 -1.2638662791
-132.5838765031 -1.1921973902
-127.8657575015 -1.1261791757
-124.4916500844 -1.0647357757
-123.016384493 -1.0070695657
-118.431306853 -0.952571595
-110.8440652315 -0.9007655189
-110.1477551652 -0.8512709934
-109.3430277914 -0.8037789242
-105.1097263145 -0.7580342264
-104.7616892077 -0.7138235056
-100.1917272772 -0.6709660579
-96.9455399284 -0.6293071641
-78.5222407532 -0.588713006
-66.833182556 -0.5490667518
-63.9367962151 -0.5102654979
-54.9666697606 -0.4722178495
-49.5089341383 -0.4348419815
-43.817663257 -0.3980640685
-30.5622414309 -0.3618169976
-29.7056802184 -0.3260393031
-28.8211160258 -0.2906742745
-21.3829190469 -0.2556692022
-20.8096302471 -0.220974732
-18.0336858908 -0.1865443062
-16.4732294274 -0.152333674
-15.5268611118 -0.1183004556
-12.5832024808 -0.0844037498
-11.5991899485 -0.0506037738
-10.6416197419 -0.0168615273
-6.4663288735 0.0168615273
6.6082090726 0.0506037738
10.1026389027 0.0844037498
10.1556691582 0.1183004556
11.5424324103 0.152333674
13.4792557233 0.1865443062
15.0213966843 0.220974732
18.9663798116 0.2556692022
19.2122025279 0.2906742745
19.5938287738 0.3260393031
19.7419844304 0.3618169976
23.7470781354 0.3980640685
25.1736217387 0.4348419815
28.9194386872 0.4722178495
38.4697564504 0.5102654979
50.9831788417 0.5490667518
53.0357068283 0.588713006
61.102903906 0.6293071641
63.1204953548 0.6709660579
63.8380153718 0.7138235056
71.0833539728 0.7580342264
71.3281648375 0.8037789242
75.1828858929 0.8512709934
75.2802525469 0.9007655189
81.3206554357 0.952571595
81.6351025536 1.0070695657
105.576464442 1.0647357757
115.0253844293 1.1261791757
122.2233804168 1.1921973902
150.1178490106 1.2638662791
180.3934285167 1.3426905457
196.2671375845 1.4308738679
205.7993140008 1.5318456091
234.8563337617 1.6514108613
289.7338930992 1.8007082352
336.0904495556 2.0061237235
372.5195939607 2.3669115357

Data

Square Feet Per Person Average Spending Sales Growth Over Previous Year (%) Loyalty Card % of Net Sales Annual Sales Per Sq Ft Median HH Income (3 Miles) Median Age (3 Miles) % w/ Bachelor’s Degree (3 Miles)
Obs SqFt Sales/Person SalesGrowth% LoyaltyCard% Sales/SqFt MedIncome MedAge BachDeg%
1 2354 6.81 -8.31 2.07 701.97 45177 34.4 31
2 2604 7.57 -4.01 2.54 209.93 51888 41.2 20
3 2453 6.89 -3.94 1.66 364.92 51379 40.3 24
4 2340 7.13 -3.39 2.06 443.04 66081 35.4 29
5 2500 7.04 -3.30 2.48 399.20 50999 31.5 18
6 2806 6.93 -1.94 2.96 264.64 41562 36.3 30
7 2250 7.11 -0.77 2.28 571.59 44196 35.1 14
8 2400 7.13 -0.37 2.34 642.25 50975 37.6 33
9 2709 6.58 -0.25 2.20 461.45 72808 34.9 28
10 1990 6.77 -0.17 2.34 638.82 79070 34.8 29
11 2392 6.66 0.47 2.09 484.38 78497 36.2 39
12 2408 7.03 0.55 2.47 581.09 41245 32.2 23
13 2627 7.03 0.77 2.04 267.71 33003 30.9 22
14 2500 7.00 1.92 2.02 572.84 90988 37.7 37
15 1986 7.38 2.05 2.01 586.48 37950 34.3 24
16 2500 7.18 2.12 2.64 368.73 45206 32.4 17
17 2668 7.35 2.84 2.22 351.47 79312 32.1 37
18 2517 6.95 2.88 2.07 458.24 37345 31.4 22
19 1251 7.02 3.96 1.94 987.12 46226 30.4 36
20 2998 6.85 4.04 2.17 357.45 70024 33.9 34
21 2625 7.16 4.05 0.72 405.77 54982 35.6 26
22 2300 6.99 4.05 2.00 680.80 54932 35.9 20
23 2761 7.28 4.24 1.81 368.02 34097 33.6 20
24 2764 7.07 4.58 2.13 303.95 46593 37.9 26
25 2430 7.05 5.09 2.50 393.90 51893 40.6 21
26 2154 6.54 5.14 2.63 562.12 88162 37.7 37
27 2400 6.70 5.48 1.95 494.88 89016 36.4 34
28 2430 6.91 5.86 2.04 310.07 114353 40.9 34
29 2549 7.58 5.91 1.41 373.46 75366 35.0 30
30 2500 7.03 5.98 2.05 235.81 48163 26.4 16
31 3653 6.84 6.08 2.13 413.08 49956 37.1 28
32 2440 6.94 6.08 2.08 625.22 45990 30.3 36
33 2600 7.07 6.13 2.73 274.30 45723 31.3 18
34 2160 7.00 6.27 1.95 542.62 43800 29.6 36
35 2800 7.08 6.57 2.04 178.56 68711 32.9 18
36 2757 6.75 6.90 1.62 375.33 65150 40.7 24
37 2450 6.81 6.94 1.95 329.09 39329 29.3 22
38 2400 7.64 7.12 1.64 297.37 63657 37.3 29
39 2270 6.62 7.39 1.78 323.17 67099 39.8 25
40 2800 6.76 7.67 2.23 468.84 75151 33.9 28
41 2520 7.11 7.91 2.15 352.57 93876 35.0 40
42 2487 7.05 8.08 2.83 380.34 79701 35.0 39
43 2629 6.90 8.27 2.37 398.12 77115 35.9 30
44 3200 7.17 8.54 3.07 312.15 52766 33.0 17
45 2335 6.75 8.58 2.19 452.16 32929 30.9 22
46 2500 7.45 8.72 1.28 698.64 87863 38.5 29
47 2449 7.00 8.75 1.76 367.19 73752 40.5 19
48 2625 6.96 8.79 2.51 431.93 85366 32.1 29
49 3150 7.30 8.90 1.90 367.06 39180 34.8 18
50 2625 6.96 9.12 1.98 400.53 56077 38.0 19
51 2741 6.71 9.47 2.41 414.36 77449 37.0 34
52 2500 6.82 10.17 2.17 481.11 56822 34.7 25
53 2450 6.58 10.66 2.16 538.06 80470 36.4 30
54 2986 7.56 10.97 0.29 330.48 55584 36.8 21
55 2967 6.98 11.34 1.85 249.93 78001 32.2 30
56 3000 7.28 11.45 1.88 291.87 75307 34.8 30
57 2500 6.76 11.51 2.19 517.40 76375 36.7 28
58 2600 6.92 11.73 2.56 551.58 61857 33.8 31
59 2800 6.73 11.83 2.16 386.81 61312 34.2 16
60 2986 6.91 11.95 2.10 427.50 72040 39.0 31
61 2223 6.77 12.47 1.98 453.94 92414 34.9 40
62 2300 7.33 12.80 0.87 512.46 92602 39.3 33
63 3799 7.87 13.78 1.07 345.27 59599 35.6 28
64 2700 6.95 14.09 3.38 234.04 72453 36.0 23
65 2650 7.33 14.23 1.17 348.33 67925 41.1 16
66 2500 6.95 14.60 2.14 348.47 42631 24.7 25
67 2994 7.21 14.88 0.93 294.95 75652 40.5 25
68 2718 7.25 15.42 2.22 361.14 39650 32.9 18
69 3700 7.65 16.18 1.68 467.71 48033 30.3 15
70 2000 6.93 17.23 2.41 403.78 67403 36.2 19
71 2400 6.79 18.43 2.81 245.74 80597 32.4 27
72 2450 7.37 20.76 1.09 339.94 60928 43.5 21
73 2575 6.76 25.54 0.64 400.82 73762 41.6 29
74 2400 7.97 28.81 1.77 326.54 64225 31.4 15

Noodles Database – Page &P of &N Printed &D Doane/Seward

Statistics homework help

Dr. Megan Zobb, a key researcher within the North Luna University Medical Center, has been studying a new variant of a skin disease virus that seems to be surfacing among the North Luna University population. This variant (which has been tentatively named Painful Rash or PR), leads to the formation of surface lesions on an individual’s body. These lesions are very similar to small boils or isolated shingles sores. These PR lesions are not necessarily clustered as shingles lesions are, but are isolated across the body.

Insights From Initial Interviews

Megan is initiating some efforts at a preliminary analysis. She has seen 20 initial patients and made several observations about the skin disease. She wants to analyze this initial data before structuring and recommending a more encompassing study.

The signs and symptoms of this disorder usually affect multiple sections of the patient’s body. These signs and symptoms may include:

· Pain, burning, numbness or tingling, but pain is always present.

· Sensitivity to touch.

· A red rash that begins a few days after the pain.

· Fluid-filled blisters that break open and crust over.

· Itching.

 Some people also experience:

· Fever.

· Headache.

· Sensitivity to light.

· Fatigue.

Pain is always the first symptom of PR. For some, it can be intense. Depending on the location of the pain, it can sometimes be mistaken for a symptom of problems affecting the heart, lungs, or kidneys. Some people experience PR pain without ever developing the rash. The degree of pain that the individual experiences is seemingly proportional to the number of lesions.

Dr. Zobb is extremely concerned that this new variant is especially challenging to the younger population, who are active and like to be outdoors. She has asked you as an analyst and statistician for some assistance in analyzing her initial data. She is not a biostatistician, so she requests that you explain the process you use and your interpretation of the results for each task.

Initial Data Analysis

Dr. Zobb has accumulated some data on an initial set of 20 patients across multiple age groups. She believes that the data suggests younger individuals are affected more than others. She wants you to complete the tasks shown here based on the data below.

For each of the following, provide a detailed explanation of the process you used along with your interpretation of the results. Submit the response in a Word document and attach your Excel spreadsheet to show your calculations (where applicable). Be sure to number each response (e.g., 1.a, 1.b,…).

1. Develop an equation to model the data using a regression analysis approach and explain your calculation process in Excel.

2. Calculate the r-square statistic using Excel.  Interpret the meaning of the r-square statistic in this case.  

3. Determine three conclusions that address the initial observations and are supported by the regression analysis.

Regression Analysis Initial Data

Patient Number

Age of Patient

Number of Lesions

1

24

16

2

63

7

3

45

12

4

17

24

5

21

20

6

72

4

7

32

13

8

36

16

9

26

21

10

47

10

11

31

15

12

23

18

13

51

8

14

24

22

15

26

18

16

25

19

17

31

12

18

19

29

19

18

25

20

21

17

 

Effects of Sunlight Analysis

In her initial observations, Dr. Zobb notices that the number of lesions that appear on a patient seems to be dependent on the amount of direct sunlight exposure that the patient receives. She is uncertain at this point why this would be the case, but she is a good experimentalist and is trying to establish some observations that have statistical validity. She has taken a limited amount of data on 8 patients and wants you to complete the appropriate analysis based on the data below (be sure to show your work):

1. Develop an equation to model the data using a regression analysis approach and explain your calculation process, using Excel.  

2. Megan has a small group of three additional patients that are the same age that she wants to examine for lesions.  She knows the number of minutes of continuous exposure to direct sunlight that each has experienced. Predict the number of lesions that each of these patients will have based on the regression analysis that you completed in your initial data analysis:

. Patient 9 – 193 minutes.

. Patient 10 – 219 minutes.

. Patient 11 – 84 minutes.

· Determine three conclusions based on the correlation of the number of lesions to minutes of sunlight exposure, using regression analysis. 

Sunlight Exposure Regression Data

Patient Number

Time of Continuous Exposure to Direct Sunlight
(Minutes)

Number of Lesions

1

225

24

2

184

16

3

220

20

4

240

26

5

180

14

6

184

16

7

186

20

8

215

22

Over the Counter Medication Effectiveness Analysis

Dr. Zobb wants to test several over the counter lotions—that is, lotions available without a prescription—that can be applied directly to the lesions. She wants to determine whether there is a difference in the mean length of time it takes these three types of pain lotions to provide relief from the pain caused by these lesions. Megan is hoping that one of these lotions might be more promising than the others. Several sufferers (with roughly the same number of lesions) are randomly selected and given one of the three medications. Each sufferer records the time (in minutes) it takes the medication to begin working. The results are shown in the table below. She asks you to answer these questions (be sure to show your work).

1. State the null hypothesis and the alternative hypothesis for this situation.

2. At α = 0.01, can you conclude that the mean times are different? Assume that each population of relief times is normally distributed and that the population variances are equal.  Hint: Use a one-way ANOVA to solve this problem. Be certain to show your calculations and describe the process you used to solve this problem.

3. Determine three conclusions on the effectiveness of the medication by addressing observations or hypotheses regarding these initial tests.

Effectiveness of Over the Counter Medications

Medication 1 (Minutes)

Medication 2 (Minutes)

Medication 3 (Minutes)

12

16

14

15

14

17

17

21

20

12

15

15

 

19

 

Summary of Data Analysis

Now that you have all of your data analysis:

1. Provide a three-paragraph summary of the findings you learned through the analysis.

2. Provide three data-driven suggestions for further exploration.

This course requires the use of Strayer Writing Standards. For assistance and information, please refer to the Strayer Writing Standards link in the left-hand menu of your course. Check with your professor for any additional instructions.

The specific course learning outcome associated with this assignment is:

· Recommend a course of action utilizing quantitative methods for health services including biostatistics, forecasting, and the modeling of predictive functions.

Statistics homework help

GRADING RUBRIC

Criterion 1

A – 4 – Mastery

Summary of notes includes a thorough explanation of what “bias” is in presentations. Skillfully provides ways to distinguish opinions from fact in presentations.

Criterion 2

A – 4 – Mastery

Thorough evaluation of poor communication and poor language in presentations.

Criterion 3

A – 4 – Mastery

Summary of best practices includes thorough suggestions for how each of the sample presentations could be improved to increase objectivity and reduce bias.

Criterion 4

A – 4 – Mastery

Provided credible, professional sources for each identified resource cited in APA format for reference page with no errors.

Statistics homework help

Week Two: Chapter Homework Calculations

Top of Form

Instructions

Chapter Homework Calculations

Week Two: Chapter Homework Calculations (i.e., show your work)

See chegg book

Required Textbook: Sullivan, L.M. (2018). Essentials of biostatistics in public health (3rd ed.). Burlington, MA: Jones & Bartlett Learning

· Chapters 3 & 4 Homework Problems: 3.1, 3.2, 3.10 & 4.18

· Chapter 5 Homework Problems: 5.4, 5.5, 5.7 & 5.10

· Chapter 6 Homework Problems: 6.4, 6.7 & 6.9

Bottom of Form

Statistics homework help

SOST10142&20142 2020-21 2nd Semester: Applied

Statistics Essay

1

SOST10142&20142 2020-21 2nd Semester : Applied Statistics Essay

Contents

1 Introduction 3

2 Exploratory Data Analysis 3

2.1 Data Source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.2 Data selection and cleaning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.3 EDA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.3.1 Person’s income . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.3.2 SCHL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.3.3 SEX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.3.4 RACWHT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.3.5 AGEP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.3.6 MAR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

3 Statistical Analysis 6

3.1 T-test to Compare Group means . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

3.1.1 The Gender Gap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

3.1.2 The Racial Gap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

3.1.3 Difference of income between educational levels. . . . . . . . . . . . . . . . . . . . . . . . 8

3.2 Odds ratios and Chi-square for categorical variables . . . . . . . . . . . . . . . . . . . . . . . . 8

3.3 Linear Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

3.4 GLM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

4 Conclusions 11

5 Discussion 11

References 12

Appendix (R code) 13

2

SOST10142&20142 2020-21 2nd Semester : Applied Statistics Essay

1 Introduction

Gender and race gap have been critical issues for social science. Also, as an essential part of our society,

economy indicates the degree of social development. People’s income level reflects the economic status of

the society. So, my interest lies on the gender and race gap in people’s income. Adrain and Emma studied

the gender difference of estimated salaries in the UK based on a between-subject design. They found that

there exists gender gap in salaries and people show good awareness of the average annual salary in the

UK.[1] Richard & Carolyn[2] and Erin & Robert[3] try to explain the racial and gender gaps for Income or

accumulated wealth in the US by taking other status (marital status, for instance) into consideration.

This essay explores the gender and racial gaps for person’s total income based on the ACS data for the

Utah state provided by the US Census Bureau. Some other possible predictors of person’s yearly total

income are also studied. The data I used contains a sample of responses of Utah state to the American

Community Survey conducted by the US Census Bureau. You can download this data set from https:

//www2.census.gov/programs-surveys/acs/data/pums/2019/1-Year/csv_put.zip. All of the R code

relative to the contents of this essay are shown in the Appendix.

2 Exploratory Data Analysis

2.1 Data Source

The data source is already mentioned in the Introduction section. The data contains some information

about the respondents in 2019 including income, educational level, sex, race, etc.

2.2 Data selection and cleaning

From this big data set (32371 observations and 288 variables, I selected 5 variables of interest and they

are summarized below:

– PINCP: person’s total income of year 2019.

– SCHL: person’s highest educational level.

– SEX: person’s gender.

– RACWHT: person’s race: White recode (White alone or in combination with one or more other races).

– AGEP: person’s age.

– MAR: person’s marital status.

After selecting these variables, I removed the missing in the data set (there were 24764 observation re-

maining after doing this). Then, I changed the levels of SCHL and MAR (from multiple levels to dummy

variable). The new level 1 of SCHL represents a bachelor’s degree or higher. The new level 0 of SCHL

represents an education level which is lower than a bachelor’s degree. The new level 1 of MAR represents

the person’s married. The new level 0 of MAR represents the person’s not married currently (either married

before but lose his/her mate or never married). Also, I created a dummy variable called CPINCP. The

high income level (denoted as 1) of CPINCP represents the person’s income is greater or equal than the 3rd

quantile. The level representing ’not high income’ (denoted as 0) of CPINCP represents the person’s income

is less than the 3rd quantile.

3

SOST10142&20142 2020-21 2nd Semester : Applied Statistics Essay

2.3 EDA

2.3.1 Person’s income

A histogram of person’s income and the summary of it are shown below. It is shown that some people are

in debt after liquidating the year’s income. Only few people have high level of income.

> summary(data$PINCP)

Min. 1st Qu. Median Mean 3rd Qu. Max.

-6600 7000 25700 42345 55000 1103000

Histogram of Person’s income

person’s income

F
re

q
u

e
n

cy

0e+00 1e+05 2e+05 3e+05 4e+05 5e+05 6e+05

0
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0
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0
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0

Figure 1: Histogram of Person’s Income

2.3.2 SCHL

The values of SCHL is shown below. 7553 of 24764 observations have bachelor’s degree or higher educa-

tional level, leading to a percentage of 30.5%.

> table(data$SCHL)

0 1

17211 7553

2.3.3 SEX

There are 12218 males among 24764 observations. The proportion is approximately a half.

> table(data$SEX)

4

SOST10142&20142 2020-21 2nd Semester : Applied Statistics Essay

1 2

12218 12546

2.3.4 RACWHT

Only 1873 observations are not white or not combined with white.

> table(data$RACWHT)

0 1

1873 22891

2.3.5 AGEP

The summary of age and its histogram are shown below. The sample size is lower in an age groups of

higher ages. This is reasonable because people die when they get older. However, this might be a problem

for our data analysis. For example, the assumption of equal variance may not be satisfied due to different

size of samples.

> summary(data$AGEP)

Min. 1st Qu. Median Mean 3rd Qu. Max.

15.00 27.00 42.00 43.98 60.00 91.00

Histogram of AGE

AGE

F
re

q
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n

cy

20 40 60 80

0
2

0
0

4
0

0
6

0
0

8
0

0
1

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0

Figure 2: Histogram of Person’s Age

5

SOST10142&20142 2020-21 2nd Semester : Applied Statistics Essay

2.3.6 MAR

Among these observations, there are currently 14546 people who are married. The proportion of married

person is 58.74%.

> table(data$MAR)

0 1

10218 14546

3 Statistical Analysis

3.1 T-test to Compare Group means

To check there exits differences of income between different group, we can use two-sample t-test. The

two-sample t-test is a method used to test whether the unknown population means of two groups are equal

or not. The general steps to perform a two-sample t-test are:

Step 1: Set the null hypothesis and the alternative hypothesis:

H0 : µ1 = µ2 v.s. Ha : µ1 6= µ2

where µ1 and µ2 are the population means of two different groups.

Step 2: Calculate the test statistic:

T =
x̄1 − x̄2

sp

1/n1 + 1/n2

where x1, x2 are sample means of different groups, n1, n2 are the sample sizes of different groups and

s2p =
((n1 − 1)s21) + ((n2 − 1)s22)

n1 + n2 − 2

where s21 and s
2
2 are sample variance of different groups.

Step 3: The test statistic follows a t distribution with degree of freedom equals to n1 + n2 − 2. Calculate
the p value and compare it to the significant level α. If p value < α, reject the null hypothesis and believe

the means for different groups are different.

3.1.1 The Gender Gap

I performed a t test in R to test the difference of income between two genders. The result is shown below.

From this result, since p value is very small (less than 0.01), we can reject the null hypothesis of no difference

and believe that people’s average income are different between different genders (male or female).

Welch Two Sample t-test

data: data$PINCP[data$SEX == 1] and data$PINCP[data$SEX == 2]

t = 40.181, df = 17987, p-value < 2.2e-16

alternative hypothesis: true difference in means is not equal to 0

95 percent confidence interval:

30280.66 33386.48

sample estimates:

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SOST10142&20142 2020-21 2nd Semester : Applied Statistics Essay

mean of x mean of y

58472.71 26639.14

However, I found a interesting phenomenon that when sliced by the marital status, the gender gap for

married population is significant while the gender gap for non married population is not significant with

significant level α = 0.01. The p-values for these two t-tests are summarized in the Table below. The

boxplots are also shown to see the difference visually. From the boxplots, we can also find that married men

earn more than non-married men.

Marital Status p value of the t test for gender gap of income

Married <2.2e-16

Not Married 0.01094

Table 1: P values for two-sample t-tests within different marital status groups

1 2

0
5

0
0

0
0

1
0

0
0

0
0

1
5

0
0

0
0

Figure 3: Boxplot of income for different gender

in married group

1 2

0
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0
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0
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0
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0
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0
0

0
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8
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0
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0

Figure 4: Boxplot of income for different gender

in non-married group

3.1.2 The Racial Gap

I performed a t test in R to test the difference of income between white race levels. The result is shown

below. From this result, since p value is very small (less than 0.01), we can reject the null hypothesis of

no difference and believe that people’s average income are different between different races (whether or not

White alone or in combination with one or more other races).

Welch Two Sample t-test

data: data$PINCP[data$RACWHT == 0] and data$PINCP[data$RACWHT == 1]

t = -10.61, df = 2446.8, p-value < 2.2e-16

alternative hypothesis: true difference in means is not equal to 0

95 percent confidence interval:

-15174.07 -10439.99

sample estimates:

mean of x mean of y

30506.73 43313.75

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SOST10142&20142 2020-21 2nd Semester : Applied Statistics Essay

3.1.3 Difference of income between educational levels.

I performed a t test in R to test the difference of income between two educational levels. The result is

shown below. From this result, since p value is very small (less than 0.01), we can reject the null hypothesis

of no difference and believe that people’s average income are different between different educational levels

(whether or not obtains a bachelor’s degree or higher).

Welch Two Sample t-test

data: data$PINCP[data$SCHL == 0] and data$PINCP[data$SCHL == 1]

t = -39.338, df = 8904, p-value < 2.2e-16

alternative hypothesis: true difference in means is not equal to 0

95 percent confidence interval:

-45163.86 -40876.49

sample estimates:

mean of x mean of y

29223.99 72244.16

3.2 Odds ratios and Chi-square for categorical variables

An odds ratio is a statistic which indicates the association between two events A and B. The odds ratio

is defined as the ratio of the odds of A in the presence of B and the odds of A in the absence of B. A and B

are independent if and only if the odds ratio is equal to 1. OR greater than 1 implies A and B are positively

correlated, OR less than 1 implies A and B are negatively correlated.

Chi-square test is used to test the independence of two categorical variables. If the null hypothesis is

accepted, the two variables are thought to be independent. Otherwise, they are not independent.

The odds ratios and results of chi-square test for dependency of income level (CPINCP) and other cate-

gorical variables are summarized in the Table below:

Other Variables Odds Ratio Chi-sq df p-value

SCHL 4.73 2702.9 1 <2.2e-16

SEX 4.00 1982.8 1 <2.2e-16

RACWHT 2.12 127.87 1 <2.2e-16

Table 2: Summary of Odds ratios and chi-square tests for association between CINCP and other categorical

variables

From the result in Table 2, all other categorical variables are dependent with income level. According

to the odds ratios, higher educational level is positively correlated with high income level; Gender ’male’

is positively correlated with high income level; White-related race is positively correlated with high income

level.

3.3 Linear Regression

A multivariate linear regression is fitted to estimate the person’s income with other variables except the

generated CPINCP being predictors. Denote this model as Model 1. The coefficients are summarized in the

Table below. From Table 3, we can find that all of the predictors are significant in Model 1.

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SOST10142&20142 2020-21 2nd Semester : Applied Statistics Essay

Model 1 Estimate Std. Error t value Pr(> |t|)
(Intercept) 15006.6807 1569.4334 9.56 0.0000

SCHL1 36053.8877 819.6811 43.99 0.0000

SEX2 -31330.5252 731.2491 -42.85 0.0000

RACWHT1 6859.8932 1385.4062 4.95 0.0000

AGEP 393.7352 19.7349 19.95 0.0000

MAR1 14566.0078 800.9325 18.19 0.0000

Table 3: Summary of coefficients for the multivariate linear regression model fitted to estimate income

Since the marital status is confounded with gender when predicting the income amount as I found in Section

3.1.1, I then fit another MLR model taking the interaction of gender and marital status into consideration.

Denoted this model as Model 2 and its coefficients are summarized in Table 4 below:

Model 2 Estimate Std. Error t value Pr(> |t|)
(Intercept) 4573.3571 1582.6639 2.89 0.0039

SCHL1 34717.8431 806.9438 43.02 0.0000

SEX2 -5792.2835 1125.4552 -5.15 0.0000

RACWHT1 6633.4287 1361.7481 4.87 0.0000

AGEP 331.2605 19.5129 16.98 0.0000

MAR1 37739.3329 1112.3476 33.93 0.0000

SEX2:MAR1 -43359.6031 1470.4108 -29.49 0.0000

Table 4: Summary of coefficients for the MLR model with interaction term

From the results in Table 4, all of the coefficients including the coefficient for the interaction term are

significant. Comparing these two models, Model 2 has a higher R2 (0.2176) over Model 1 (0.1902). Thus,

Model 2 can explain more variance of people’s income and it’s the better choice.

0e+00 4e+04 8e+04


2

0
0

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Fitted values

R
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si
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ls

Residuals vs Fitted

20339
20338

28639

−4 −2 0 2 4

0
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1
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Theoretical Quantiles

S
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Normal Q−Q

20339
20338

28639

Figure 5: Residual plots of Model 2 for assumption checking

9

SOST10142&20142 2020-21 2nd Semester : Applied Statistics Essay

Next, I performed assumption checking for Model 2, the residual plots are shown in Figure 5. According

to the fist plot, most of the residual values are concentrated near 0. However, it shows an slightly increasing

pattern of variance. Thus, the assumption of equal variance may be slightly violated. The QQ plot shows a

violation of normality. The right tail of our residuals are much heavier than the normal distribution. Also,

there are several outliers shown in the residual plots.

3.4 GLM

In this section, a logistic regression is fitted to classify whether a given person is at high level of income or

not. The reason for using a logistic regression is that CPINCP is a dummy variable and logistic regression is

a well-designed classifier for non-linear binary response. The core idea of logistic regression is to use a link

function to transfer the linear part into values between 0 and 1. The independent variables are all variables

in our data set except PINCP and CPINCP and I also took the interaction of gender and marital status into

consideration. The coefficients of this model are summarized below in Table 3.

Estimate Std. Error z value Pr(> |z|)
(Intercept) -3.1370 0.0889 -35.30 0.0000

SCHL1 1.4712 0.0352 41.80 0.0000

SEX2 -0.4877 0.0627 -7.78 0.0000

RACWHT1 0.6130 0.0752 8.15 0.0000

AGEP 0.0125 0.0009 13.39 0.0000

MAR1 1.4802 0.0507 29.18 0.0000

SEX2:MAR1 -1.5349 0.0759 -20.21 0.0000

Table 5: Summary of coefficients for the fitted logistic regression model

From Table 5, we can find that all the coefficients in this model are significant, meaning all predictors are

powerful to help logistic regression classifying high income level. Take age for example, the log-odds of the

person being high income level will be increase by 0.0125 in average if the person’s age is increased by 1,

holding other variables constant.

−3 −2 −1 0 1


2

0
2

4
6

Predicted values

R
e

si
d

u
a

ls

Residuals vs Fitted

296082189628867

−4 −2 0 2 4


2

0
2

4
6

Theoretical Quantiles

S
td

.
P

e
a

rs
o

n
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e
si

d
.

Normal Q−Q

29608 2189628867

Figure 6: Residual plots of the logistic regression for assumption checking

10

SOST10142&20142 2020-21 2nd Semester : Applied Statistics Essay

Next, the residual plots of this logistic regression model to check the assumptions. They are shown in

Figure 6 above. The first plot shows that the residuals are biased towards the positive part. The QQ plot

does not show a normal pattern (with the right tail being heavier than the normal distribution). Also, there

are several outliers shown in the residual plots.

4 Conclusions

This report exams the relationship of several variables with a person’s yearly income. It shows that for

the population in Utah State of the US, educational level, gender and race (white or not) are all powerful

influential factor of person’s yearly income. In other words, there exists gender and racial gaps of total yearly

income. Also, age is a good predictor for estimating the person’s yearly income. And all of these variables

are powerful predictors for classifying whether the person is at high income level.

5 Discussion

Here, I want to talk a little bit about the violation of assumptions in the MLR and GLM models. This

is somewhat related to the original method of data collecting. Really high incomes are top coded when

performing the ACS survey. That’s why we see a fault in the values of Y. Also, the normality assumption is

violated because the distribution of incomes does not appears to be normal. For example, there are several

people with extremely high incomes while there are little chance to find a person with extremely high loan.

11

SOST10142&20142 2020-21 2nd Semester : Applied Statistics Essay

References

[1] Furnham, Adrain, and Emma Wilson. “Gender Differences in Estimated Salaries: A UK Study.” The

Journal of Socio-Economics, vol. 40, no. 5, 2011, pp. 623–630., doi:10.1016/j.socec.2011.04.019.

[2] Hogan, Richard, and Carolyn C. Perrucci. “Producing and Reproducing Class and Status Differences:

Racial and Gender Gaps in U.S. Employment and Retirement Income.” Social Problems, vol. 45, no. 4,

1998, pp. 528–549., doi:10.1525/sp.1998.45.4.03x0179w.

[3] Ruel, Erin, and Robert M. Hauser. “Explaining the Gender Wealth Gap.” Demography, vol. 50, no. 4,

2012, pp. 1155–1176., doi:10.1007/s13524-012-0182-0.

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SOST10142&20142 2020-21 2nd Semester : Applied Statistics Essay

Appendix (R code)

rm(list = ls())

# read the data

data_utah = read.csv(’psam_p49.csv’, header = T)

# select variables of interest

data = data_utah[,c(’PINCP ’, ’SCHL’, ’SEX’, ’RACWHT ’, ’AGEP’, ’MAR’)]

# remove NA

data = data [!(is.na(data$PINCP)),]

data$SCHL = as.numeric(data$SCHL >=21)

data$MAR[data$MAR!=1] = 0

data$CPINCP = as.numeric(data$PINCP >=55000)

# EDA

## person ’s income

hist(data$PINCP ,50, xlim = c(-2e4,6e5), xlab = “person ’s income”,

main = “Histogram of Person ’s income”)

summary(data$PINCP)

## SCHL

table(data$SCHL)

## SEX

table(data$SEX)

## RACWHT

table(data$RACWHT)

## AGEP

hist(data$AGEP , 50, xlab = ’AGE’, main = ’Histogram of AGE’)

# 3

## T-test

### education level

t.test(data$PINCP[data$SCHL==0],data$PINCP[data$SCHL==1])

### gender gap

t.test(data$PINCP[data$SEX==1],data$PINCP[data$SEX==2])

t.test(data$PINCP[data$MAR==1 & data$SEX==1],

data$PINCP[data$MAR==1 & data$SEX==2])

boxplot(data$PINCP[data$MAR==1 & data$SEX==1],

data$PINCP[data$MAR==1 & data$SEX==2],outline = F)

t.test(data$PINCP[data$MAR!=1 & data$SEX==1],

data$PINCP[data$MAR!=1 & data$SEX==2])

boxplot(data$PINCP[data$MAR!=1 & data$SEX==1],

data$PINCP[data$MAR!=1 & data$SEX==2],outline = F)

### racial gap

t.test(data$PINCP[data$RACWHT ==0],data$PINCP[data$RACWHT ==1])

## Odds ratio

p1 = sum(data$SCHL==1&data$CPINCP ==1)/sum(data$CPINCP ==1)

13

SOST10142&20142 2020-21 2nd Semester : Applied Statistics Essay

p2 = sum(data$SCHL==1&data$CPINCP ==0)/sum(data$CPINCP ==0)

p1/(1-p1)/((p2/(1-p2)))

p1 = sum(data$SEX==1&data$CPINCP ==1)/sum(data$CPINCP ==1)

p2 = sum(data$SEX==1&data$CPINCP ==0)/sum(data$CPINCP ==0)

p1/(1-p1)/((p2/(1-p2)))

p1 = sum(data$RACWHT ==1&data$CPINCP ==1)/sum(data$CPINCP ==1)

p2 = sum(data$RACWHT ==1&data$CPINCP ==0)/sum(data$CPINCP ==0)

p1/(1-p1)/((p2/(1-p2)))

## chi -sq test

chisq.test(data$CPINCP , data$SEX)

chisq.test(data$CPINCP , data$RACWHT)

chisq.test(data$CPINCP , data$RACWHT)

## linear regression

mlinear = lm(PINCP~.-CPINCP , data)

summary(mlinear)

minter = lm(PINCP~.-CPINCP+SEX*MAR , data)

summary(minter)

par(mfrow = c(1,2))

plot(minter , which = 1:2)

library(xtable)

xtable(summary(mlinear ))

## logistic regression

for (i in c(“SCHL”, “MAR”, “SEX”, “RACWHT”)){

data[,i] = as.factor(data[,i])

}

mlogit = glm(CPINCP~.-PINCP+SEX*MAR , data , family = ’binomial ’)

summary(mlogit)

plot(mlogit , which = c(1,2))

xtable(summary(mlogit ))

14

  • 1 Introduction
  • 2 Exploratory Data Analysis
    • 2.1 Data Source
    • 2.2 Data selection and cleaning
    • 2.3 EDA
      • 2.3.1 Person’s income
      • 2.3.2 SCHL
      • 2.3.3 SEX
      • 2.3.4 RACWHT
      • 2.3.5 AGEP
      • 2.3.6 MAR
  • 3 Statistical Analysis
    • 3.1 T-test to Compare Group means
      • 3.1.1 The Gender Gap
      • 3.1.2 The Racial Gap
      • 3.1.3 Difference of income between educational levels.
    • 3.2 Odds ratios and Chi-square for categorical variables
    • 3.3 Linear Regression
    • 3.4 GLM
  • 4 Conclusions
  • 5 Discussion
  • References
  • Appendix (R code)

Statistics homework help

GRADING RUBRIC

Criterion 1

A – 4 – Mastery

Summary of notes includes a thorough explanation of what “bias” is in presentations. Skillfully provides ways to distinguish opinions from fact in presentations.

Criterion 2

A – 4 – Mastery

Thorough evaluation of poor communication and poor language in presentations.

Criterion 3

A – 4 – Mastery

Summary of best practices includes thorough suggestions for how each of the sample presentations could be improved to increase objectivity and reduce bias.

Criterion 4

A – 4 – Mastery

Provided credible, professional sources for each identified resource cited in APA format for reference page with no errors.

Statistics homework help

RUBRIC

Criterion 1

A – 4 – Mastery

Skillfully identifies stakeholder/audience groups and provides a thorough focus on the importance of meeting their needs and goals.

Criterion 2

A – 4 – Mastery

Thorough evaluation of the audience member’s background and skills.

Criterion 3

A – 4 – Mastery

Thorough definition of factors which may motivating or influence the audience.

Criterion 4

A – 4 – Mastery

Thorough comparison and contrast of “how to” present data to this particular audience and “how not to” present data to this particular audience. Provide at least one example of each.

Statistics homework help

Week Two: Chapter Homework Calculations

Top of Form

Instructions

Chapter Homework Calculations

Week Two: Chapter Homework Calculations (i.e., show your work)

See chegg book

Required Textbook: Sullivan, L.M. (2018). Essentials of biostatistics in public health (3rd ed.). Burlington, MA: Jones & Bartlett Learning

· Chapters 3 & 4 Homework Problems: 3.1, 3.2, 3.10 & 4.18

· Chapter 5 Homework Problems: 5.4, 5.5, 5.7 & 5.10

· Chapter 6 Homework Problems: 6.4, 6.7 & 6.9

Bottom of Form

Statistics homework help

Monte Carlo Simulation

Monte Carlo simulation basics

• Random number generator
• Start with unit uniform random number (r)

• r is uniformly distributed from 0 to 1

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0

X

f(x)

Unit, Uniform random number generator

• Excel
• RAND()

• Basic
• RND

• Do not use random between
• There is not enough discrimination

Procedure for generating
1000 Uniform random numbers in Excel

A1:A1000

Step 1 Step 2 Step 3

Input formula for random
number “=Rand()” in cell A1

Copy and paste the
formula from A1 and
type here A1:A1000,
press <ENTER> twice.

1000 Uniform random
numbers are generated.
Press F9 several times to
generate a new set.

Exercise: Simulate flipping a coin

• Simulate
• 10 coin flips

• 100 coin flips

• 1000 coin flips

• 10 000 coin flips

• Use the running average

• How many coin flips do you need to be within 1% deviation:
49% and 51%

How many trials?

• Steady-state
• A steady-state solution is reached when the output of the simulation from one iteration

to the next changes negligibly

• When calculating means and variances: 1 000 iterations is usually sufficient

• If calculating confidence limits, many more iterations are required; after all, for 99%
confidence limits the sample size for the number of random deviates exceeding the
confidence limit is 1/100th the number of iterations

• How many coin flips are needed to reach steady-state?

• What is your error?

• Take coin flipping example to steady state

Simulation of 1000 coin flips in Excel

Use formula “=IF(RAND()<0.5,1,0)”

Generating random numbers

• Set r equal to F(x) for the desired distribution and solve for x

• Exponential distribution example

ln(r)
1

-x

r)-ln(1
-x

x-r)-ln(1

er-1

e-1r
x

x-

λ

λ

λ

λ

λ

=

=

=

=

=

Normal random number generators

• Excel
• Use the Normal inverse function

• =NORM.INV(RAND(),MEAN,STD)

• Slow with large data sets

• Uses numerical integration

• Fast alternative <Random2.xls>

( ) μσπ += )rcos(2)2ln(r-x
21

Simulate a Normal random variable

• Mean = 50

• Standard deviation = 4

• Generate 1000 random numbers with Excel

• Verify in Jasp or another software package

• How many outliers?

Circuit example

•P = V2/R
• Voltage (V) is Normally distributed

• mean = 12

• standard deviation = 0.1

• Resistance (R) is Normally distributed
• mean = 2

• standard deviation = 0.2

Where does input data come from?

• Current production

• Supplier

• Discuss how to obtain mean and standard deviation for voltage and resistance

Circuit example

1. What does the power distribution look like?
• Specifications

• 72 ± 10

• Will this circuit design meet specifications?

2. Change standard deviation of voltage to 0.3 and standard deviation of
resistance to 0.4

• What is the mean and standard deviation of power?

3. Change standard deviation of voltage to 0.5 and standard deviation of
resistance to 0.6

Summary

• Simulation can be used to model systems when inputs are known

• Verify all inputs

• Validate models

• Models may be useful even if incomplete

Statistics homework help

RUBRIC

Criterion 1

A – 4 – Mastery

Skillfully identifies stakeholder/audience groups and provides a thorough focus on the importance of meeting their needs and goals.

Criterion 2

A – 4 – Mastery

Thorough evaluation of the audience member’s background and skills.

Criterion 3

A – 4 – Mastery

Thorough definition of factors which may motivating or influence the audience.

Criterion 4

A – 4 – Mastery

Thorough comparison and contrast of “how to” present data to this particular audience and “how not to” present data to this particular audience. Provide at least one example of each.

Statistics homework help

Unit 4: Report Writing
Research Report

THE CHANGE IN THE AUSTRALIAN WORK FORCE SINCE THE
END OF WORLD WAR II

Prepared by: NAME SURNAME

Preparation for Tertiary Studies Course
Victorian University of Technology

Lecturer: NAME SURNAME

2nd September 2001

Version 1.0
Concurrent Study Research Report Page 1

Summary

This report discusses the changes that have occurred in the Australian workforce since
the end of World War II (1945-2000). A review of some of the available literature
provides insights into the changing role of women and migrants in the workforce, and the
influence of new technologies and changing levels of unemployment have also been
considered.

Key findings include:

There has been a marked increase in women’s participation in the workforce,
particularly that of married women.

While immigration was encouraged in post-war Australia as a way of providing
labour for new industries and major projects, the migrant population continues to
experience a high rate of unemployment in low-skilled jobs.

During the period 1945-2000, the nature of work in Australia has changed with a shift
from labour-intensive rural and manufacturing industries to ‘white collar’ industries
like tourism and entertainment.

The number and proportion of unemployed people in Australia has risen dramatically,
and factors that influence a person’s likelihood of experiencing unemployment
include age, proficiency in speaking English, and geographic location.

The information presented in this report has been gathered from secondary sources, and
from Australian Bureau of Statistics’ data.

The report has been prepared for submission as Unit 4 of the Tertiary Studies Course at
Victoria University.

Version 1.0
Concurrent Study Research Report Page 2

TABLE OF CONTENTS

Summary 2

1 Introduction 4

2 Findings 5

2.1 Women’s Workforce Participation Rate
Table 1. Proportion of women in the manufacturing industry 5

2.2 Migrant Workers’ Participation Rates 6
2.3 Employment Categories 7
2.4 Unemployment and Demographic Factors 8

3 Conclusion 10

4 Recommendation 10

5 Reference List 11

6 Appendix A: Employment by Industry, 1970-1995 12

Version 1.0
Concurrent Study Research Report Page 3

1 Introduction

The profile of the Australian workforce has a ltered markedly since the end of World War
II. Australia has transform ed from a nation of predom inantly Anglo-Celtic cultu re and
almost full em ployment to one of rich cultural diversity with relatively high
unemployment. This report exam ines ways in which our workforce has changed,
focusing on the f ollowing categories: women’s workforce participation rates, m igrant
workers’ participation rates, e mployment categories, unemployment rates and
demographic profiles. This repor t will also consider n ew influences affecting the
workforce.

This report is an assessable com ponent of th e Preparation for Tertiary Studies course at
Victoria University of Technology, Werribee Campus.

1.1 Methodology

Information for this report was sourced from various secondary sources, all listed in the
Reference List. Data from publications by the Australian Bureau of Statistics also proved
valuable. This report is not a comprehensiv e review of the ava ilable literature, but
provides a broad overview of the topic.

1.2 Scope of the report

Wherever the term ‘workforce’ on its own is u sed, it is in reference to the Austr alian
workforce. Where the infor mation refers to a particular state, th is will be noted. The
period under consideration is 1945 to 2000, alt hough where available data does not cover
the entire period, this is stated. The re port focuses on several key aspects of the
Australian workforce, and is not a com prehensive account of al l changes that have
occurred in the workforce since World War II.

Version 1.0
Concurrent Study Research Report Page 4

2. Findings

2.1 Women’s Workforce Participation Rates

The overall participation rate of women in the Australian workforce since the end
of World War II has in creased markedly. The absence of m ale workers during the
war ‘brought into the workforce considerable numbers of women who had not been
employed before the war broke out’ (Ryan and Conlon 1989, p. 137). However,
many women gave up their jobs when the men returned. Their rates of pay
compared to men were reduced in th e post-war years (R yan and Conlon 1989, pp.
140-144). Edna Ryan and Anne Conlon provi de the following table, which shows
that the proportion of wom en in the manufacturing industry peaked during the war,
declined until 1959, and then began to increase gradually.

Table 1. Proportion of women in the manufacturing industry.

Males to every
100 females

1932-3 239
1938-9 271
1943-4 237
1944-5 250
1947-8 308
1951-2 315
1954-5 325
1957-8 327
1958-9 330
1961-2 326
1962-3 319

Over the next 29 years, cam paigns for equal pay (or at leas t for better than 75 per
cent of the male rate for the same work) took place across many industries, and this
was achieved in principle in 1974 (Ryan and Conlon 1989, ch. 6).

In 1945, 24 per cent of the workforce in Australia was women (Zajdow 1995, p. 3).
By 1947, this had dropped back to 22.4 per cent. In 1973, this had increased to 33
per cent (Ryan and Conlon 1989, p. 174). In 1993, wom en made up 52 per cent of
the workforce (Zajdow 1995, p. 3).

The increase in married women in the workforce has been particularly marked.

‘In 1947 only 15.3 per cent of wom en in the female labour force were
married, or 3.4 per cent of the tota l labour force. In 1971 56.8 per cent
of women in the fem ale labour force were m arried, or 18 per cent of
the total labour force.’ (Ryan and Conlon 1989, p. 174)

Version 1.0
Concurrent Study Research Report Page 5

Married women’s participation increased ra pidly after 1971. This is due, in part, to
the fact that until the 1950s, women in government employment, including teachers
and university staff, had been required to leave their jobs upon m arrying. In 1971,
36 per cent of all m arried women were in paid work. In 1995, 55 per cent of all
married women were in paid work. During this time, the proportion of men in paid
work declined by 10 per cen t, and the proportion of un married women has stayed
the same (Norris and Wooden 1996, p. 2).

Much of the growth in wom en’s employment has occurred as wom en have moved
from the ‘feminine’ careers of teaching a nd nursing into resp ectable ‘white collar’
industries such as banking and retailing (Game and Pringle 1983, p. 19).

Participation in the work force is uneven across different groups of wom en such as
sole parents and Aboriginal and Torres St rait Islanders who have lower rates of
participation. However, the particip ation rate of wom en in ge neral is higher now
than at the conclusion of World War II (Zajdow 1995, p3; Ryan and Conlon 1989,
p. 174).

2.2 Migrant Workers’ Participation Rates

The years since the end of the S econd World War have seen an increase in
immigration into Austra lia and the refore an incr ease in the num ber of migrants in
the workforce. Post-war Australia saw th e rapid national developm ent of projects
such as the Snowy Mountains Hydro-Electric Scheme. This meant a great dem and
for labour, which the Australian workforce could not fulfil at the tim e. Migrants
were therefore encouraged to come to Australia to f ill such jobs, res ulting in a
period of high migrant employment (Carroll 1989, p. 48).

Workers born overseas now constitute a s ubstantial proportion of the workforce;
however, this group does suffer a high une mployment rate. Some of the reasons for
this include their lack of proficiency in English, the undervaluing or lack of
recognition of qualifications received overseas, the lack of a verifiable employment
‘history’ with which to impress employers, discrimination and under-representation
in trade unions (VandenHeuvel and Wooden 1996, pp. 7-8). All of these factors are
more pronounced among non-English speaking background (NESB) women.

‘Prior to the 1980s, the convent ional wisdom was that NESB
immigrants, including wom en, had higher rates of labour force
participation than their Australia- born counterparts… By the early
1980s, however, this situation had dr amatically altered, such that
labour force participation rates of both NESB men and women now lie
well below that of Australia-born men and wom en.’ (VandenHeuvel
and Wooden 1996, p. 10)

Version 1.0
Concurrent Study Research Report Page 6

The large increase in married women in the workforce applies only to Austra lia-
born women (a 14 per cent increase from 1980-94), and English-speaking
background (ESB) m igrants (a 9.7 per cen t increase). The proportion of m arried,
NESB migrant women in the labour force dropped slightly over the period
(VandenHeuvel and Wooden 1996, p. 10). Wo rkforce participation for NESB
women varies depending on their country of origin, but overall, their participation
has decreased (VandenHeuvel and Wooden 1996, p. 11).

Unemployment rates for NESB women show that in 1980 there was little difference
from the unemployment rate of 7-8 per cent for women regardless of their country
of birth (including Australia). By 1994, fi gures for Australia-born and ESB wom en
were still at that level, while the ra te for NESB women had peaked at o ver 16 per
cent in 1993 before falling to 15 per cent (VandenHeuvel and Wooden 1996, p. 15).

Post-war Australia saw a dramatic increa se in immigration; however, the migrant
population does experience a high degree of unemployment and participation in
lower-skilled jobs compared to people born in Australia.

2.3 Employment Categories

The major types of employm ent dominating the workforce at th e conclusion of
World War Two differ greatly from the categories of employm ent available in
recent times. After 1945, the Governm ent encouraged m anufacturing. This was
initially to provide employment for returned servicemen, then later to lower imports
as a m eans to ease its balance o f payment difficulties. Rural ind ustries also
prospered at this tim e due to a short supply of food and basic commodities in
countries badly ravaged by the war. By 1950, 28 per cent of Australians were
employed in secondary industries and 17 per cent in prim ary industries (Carroll
1989, p48). The proportion of Australians employed in these areas has since fallen.

In the early 1970s, the governm ent reduced tariffs for pri mary exports in an effort
to enter into trade agreem ents with Asian countries. This w as followed soon after
by a recession, and th e markets that the gov ernment had hoped to reach with their
manufactured goods dried up. Australian ru ral and m ining industries also suffered
and this reduced em ployee numbers. In the early 1980s, a severe drought and
another economic slump once again reduced employment opportunities in prim ary
industries (Carroll 1989, p56).

From 1970 to 1995, the percentage of the to tal workforce engaged in agriculture
and mining dropped from 9.6 per cent to 6 per cent. The proportion of the
workforce engaged in m anufacturing dropped from 24.5 per cent to 13.6 per cent.
The services industry, including occupati ons like hairdressing, entertainment,
hospitality and tourism , has seen signif icant growth during the sam e period. The
proportion of the workforce engaged in services has increased from 47.8 per cent to
65.7 per cent. (Norris and W ooden 1996, p. 6). See Appendix A for a fi ve-yearly
breakdown of these shifts.

Version 1.0
Concurrent Study Research Report Page 7

As the end of the cen tury drew closer, entirely new types of employment emerged
and are still growing. Many labour-intensive industrial jobs are now automated and
performed by com puters, microprocessors or robots. Inform ation technology is
quickly becoming a growing area of em ployment in Austra lia with m any jobs
centred around the selling, servicing, pr ogramming and operating of com puters
(Carroll 1989, p. 56).

The Australian workforce has gone from being largely based around manufacturing
and exporting to being largely based around importing and consumerism.

2.4 Unemployment and Demographic Rates

Australia has experienced a dram atic increase in the rate o f unemployment since
the end of World W ar Two. At that tim e, and for approxim ately the next thirty
years, unemployment was virtually non-exis tent and work was readily available
(Carroll 1989, p. 48). In 1970, the unem ployment rate was 1.5 per cent of the
labour force, and the underem ployment rate was less than 1 per cent (N orris and
Wooden 1996, p. 8). U nderemployment is defined as part-tim e workers who would
prefer to work m ore hours and full-tim e workers who worked less than their usual
hours for economic reasons.

This is in contrast to current tr ends. Between 1970 and 1995, underemploym ent
rose fairly steadily to 7 per cent of the total labour force, while unemployment rose
in three dramatic jumps in the m id-1970s (to 4 per cent), the early 1980s (to 9 pe r
cent) and the early 1990s (to 10 per cent). The late 1980s saw the unemploym ent
rate drop back to less than 6 per cent and, after peaking again at over 10 per cent in
the interim, in 1998, the unem ployment rate had fallen to eight percent (Australian
Bureau of Statistics 1999; Norris and Wooden 1996, p. 8). It is not uncommon for
job seekers to be without em ployment for several years at a tim e. In 1994, 35 per
cent of unemployed people had experienced long-term unemployment. This rate
has decreased since that tim e (Norris and Wooden 1996, p. 9). A range of
demographic factors and indicators affects the current high rate of unemployment.

Several factors determ ine a person’s likel ihood of experiencing unem ployment in
the current working clim ate. These in clude socio-economic background, area of
residence (rural versus urban areas), prof iciency in speaking English, age, and to a
lesser degree, sex.

The following data was obtained by the Au stralian Bureau of Statistics in
September 1997, and pertains to job seekers nation wide. At this tim e, an average
of twenty-seven percent of job seekers from the lowest socio-economic background
had not worked at all, com pared to seventeen p ercent of those from higher socio-
economic areas. The proportion of job seek ers that had not worked since May 1995
was highest in m ajor urban areas (27 per cent) and lowest in rural areas (20 pe r
cent). There is also a solid link betw een a person’s lack of prof iciency in speaking

Version 1.0
Concurrent Study Research Report Page 8

English and unem ployment. Sixty one per cent of persons who do not speak
English proficiently or at all had been unemployed since 1995. It also appears that
the older a person is, the greater the chan ce of being unem ployed for a long period
of time. Forty three per cent of job seekers between the ag es of forty-five to fifty-
nine had not worked since May 1995. Fifty per cent of these people reported that
they were considered to be too old by employers. Virtually the same proportions of
male and fe male job seekers were in stable em ployment at Septem ber 1997. The
only variation was that f or males, this work was predominantly full-time, while for
females, half were working part-time (Australian Bureau of Statistics 1997, p. 20).

In a period of fifty-five years, Australian has tr ansformed from a nation of
practically no unemployment to one of reasonably high unemployment with rather
complex and varied causes.

Version 1.0
Concurrent Study Research Report Page 9

3. Conclusion

The Australian workforce has altered greatly in the fifty-five years since the end of World
War II. Many of these changes have been very positive, such as the growth of women in
the workforce, the formation of many new employment categories and the introduction of
migration to cope with a tim e of great industr ial growth, which has in turn enriched our
culture.

There are, however, som e negative aspects associated with the transf ormation. Many
areas of employment have been replaced by m achinery or other technologies, displacing
unskilled workers. Consequently, Australian society is now experiencing a high dem and
for a skilled labour force, and an increasing se ctor of the population without such skills is
suffering long-term unemployment. The change experienced in such a relatively short
period of time leads to the question: what do the next fifty-five years hold?

4. Recommendation

The information collected for this report provides a broad overview of key changes in the
Australian workforce. Further analysis would be possible if the relevant data for each
year from 1945-2000 was purchased from the Australian Bureau of Statistics. The
reliance on secondary sources has resulted in some patchy data. For example, it is not
possible to identify for any given year a breakdown of the Australian workforce by the
following categories:

• unmarried Australia-born women
• married Australia-born women
• unmarried Australia-born men
• married Australia-born men
• unmarried immigrant women
• married immigrant women
• unmarried immigrant men
• married immigrant men

Greater access to primary data would enable a more thorough analysis to be made.

Version 1.0
Concurrent Study Research Report Page 10

5. Reference List

Australian Bureau of Statistics 1997, Australians, Employment and Unemployment
Patterns: 1994-1997, ABS, Canberra.

Australian Bureau of Statistics 1999, Year Book Australia 1998, ABS, Canberra.

Carroll, B. 1989, Australians at Work through 200 Years, Kangaroo Press, Sydney.

Game, A. and Pringle, R. 1983, Gender at Work, George Allen & Unwin Australia Pt y
Ltd, North Sydney.

Norris, K. and W ooden, M. (eds.) 1996, The Changing Australian Labour Market,
Economic Planning Ad visory Committee, Australian Governm ent Publishing Service,
Canberra.

Ryan, E. and Conlon, A. 1989 (1975), Gentle Invaders: Australian Women at Work,
Penguin Books Australia, Ringwood.

VandenHeuvel, A. and Wooden, M. 1996, Non-English-speaking-background immigrant
women and part-time work, Bureau of I mmigration, Multicultural and Population
Research, Carlton South.

Victorian Ethnic Affairs Comm ission 1984, Migrants and the Workforce, VEAC,
Melbourne.

Zajdow, G. 1995, Women and Work – Current Issues and Debates, Deakin University
Press, Geelong.

Version 1.0
Concurrent Study Research Report Page 11

6. Appendix

Appendix A: Employment by Industry, 1970-1995 (% of total employment)

1970 1975 1980 1985 1990 1995
Agriculture and
mining

9.6 8.2 7.8 7.7 6.6 6.0

Manufacturing 24.5 21.6 19.7 16.7 15.3 13.6
Utilities,
construction,
transport &
communication

18.1 18.3 17.2 17.1 15.8 14.7

Services 47.8 52.0 55.4 58.6 62.3 65.7

Table from Norris and Wooden 1996, p. 6.

Version 1.0
Concurrent Study Research Report Page 12

  • Research Report
    • Summary
    • TABLE OF CONTENTS
      • Summary 2
      • 1 Introduction 4
        • 3 Conclusion 10
        • 4 Recommendation 10
          • 1.2 Scope of the report
            • Appendix A: Employment by Industry, 1970-1995 (% of total employment)

Statistics homework help

As a professional in the real world, you will need to research and understand various aspects of Business applications. Basic statistical analysis can be used to gain an understanding of current problems. This course project will assist you in applying basic statistical principles to a fictional scenario in order to impact the clients being served.

A major client of your company is interested in the salary distributions of jobs in the state of Georgia that range from $40,000 to $120,000 per year. As a Business Analyst your boss asks you to research and analyze the salary distributions. You are given a spreadsheet that contains the following information:

· A listing of the jobs by title

· The salary (in dollars) for each job

The client needs the preliminary findings by the end of the day. So let’s get to work!!!!

The data set consists of 364 records that you will be analyzing from the Bureau of Labor Statistics. The data set contains a listing of several jobs titles with yearly salaries ranging from approximately $40,000 to $120,000 for the state of Georgia.

Statistics homework help

Monte Carlo Simulation

Monte Carlo simulation basics

• Random number generator
• Start with unit uniform random number (r)

• r is uniformly distributed from 0 to 1

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0

X

f(x)

Unit, Uniform random number generator

• Excel
• RAND()

• Basic
• RND

• Do not use random between
• There is not enough discrimination

Procedure for generating
1000 Uniform random numbers in Excel

A1:A1000

Step 1 Step 2 Step 3

Input formula for random
number “=Rand()” in cell A1

Copy and paste the
formula from A1 and
type here A1:A1000,
press <ENTER> twice.

1000 Uniform random
numbers are generated.
Press F9 several times to
generate a new set.

Exercise: Simulate flipping a coin

• Simulate
• 10 coin flips

• 100 coin flips

• 1000 coin flips

• 10 000 coin flips

• Use the running average

• How many coin flips do you need to be within 1% deviation:
49% and 51%

How many trials?

• Steady-state
• A steady-state solution is reached when the output of the simulation from one iteration

to the next changes negligibly

• When calculating means and variances: 1 000 iterations is usually sufficient

• If calculating confidence limits, many more iterations are required; after all, for 99%
confidence limits the sample size for the number of random deviates exceeding the
confidence limit is 1/100th the number of iterations

• How many coin flips are needed to reach steady-state?

• What is your error?

• Take coin flipping example to steady state

Simulation of 1000 coin flips in Excel

Use formula “=IF(RAND()<0.5,1,0)”

Generating random numbers

• Set r equal to F(x) for the desired distribution and solve for x

• Exponential distribution example

ln(r)
1

-x

r)-ln(1
-x

x-r)-ln(1

er-1

e-1r
x

x-

λ

λ

λ

λ

λ

=

=

=

=

=

Normal random number generators

• Excel
• Use the Normal inverse function

• =NORM.INV(RAND(),MEAN,STD)

• Slow with large data sets

• Uses numerical integration

• Fast alternative <Random2.xls>

( ) μσπ += )rcos(2)2ln(r-x
21

Simulate a Normal random variable

• Mean = 50

• Standard deviation = 4

• Generate 1000 random numbers with Excel

• Verify in Jasp or another software package

• How many outliers?

Circuit example

•P = V2/R
• Voltage (V) is Normally distributed

• mean = 12

• standard deviation = 0.1

• Resistance (R) is Normally distributed
• mean = 2

• standard deviation = 0.2

Where does input data come from?

• Current production

• Supplier

• Discuss how to obtain mean and standard deviation for voltage and resistance

Circuit example

1. What does the power distribution look like?
• Specifications

• 72 ± 10

• Will this circuit design meet specifications?

2. Change standard deviation of voltage to 0.3 and standard deviation of
resistance to 0.4

• What is the mean and standard deviation of power?

3. Change standard deviation of voltage to 0.5 and standard deviation of
resistance to 0.6

Summary

• Simulation can be used to model systems when inputs are known

• Verify all inputs

• Validate models

• Models may be useful even if incomplete

Statistics homework help

Sheet1

Job Title Salary
Accountants and Auditors 63,910 source: http://www.bls.gov/
Actuaries 84,190
Administrative Law Judges, Adjudicators, and Hearing Officers 117,110
Administrative Services Managers 94,450
Adult Basic and Secondary Education and Literacy Teachers and Instructors 43,500
Advertising and Promotions Managers 75,710
Advertising Sales Agents 46,100
Aerospace Engineering and Operations Technicians 59,800
Aerospace Engineers 104,730
Agents and Business Managers of Artists, Performers, and Athletes 77,690
Agricultural and Food Science Technicians 44,470
Agricultural Inspectors 43,470
Agricultural Sciences Teachers, Postsecondary 92,010
Air Traffic Controllers 94,030
Aircraft Cargo Handling Supervisors 44,890
Aircraft Structure, Surfaces, Rigging, and Systems Assemblers 42,410
Airfield Operations Specialists 52,740
Airline Pilots, Copilots, and Flight Engineers 98,480
Anthropologists and Archeologists 43,970
Appraisers and Assessors of Real Estate 50,150
Arbitrators, Mediators, and Conciliators 56,700
Architects, Except Landscape and Naval 75,440
Architectural and Civil Drafters 46,470
Architecture and Engineering Occupations 79,910
Architecture Teachers, Postsecondary 79,040
Archivists 60,560
Art Directors 76,280
Art, Drama, and Music Teachers, Postsecondary 57,210
Athletic Trainers 42,330
Atmospheric and Space Scientists 84,390
Atmospheric, Earth, Marine, and Space Sciences Teachers, Postsecondary 92,630
Audiologists 53,830
Avionics Technicians 56,440
Biomedical Engineers 85,810
Boilermakers 55,870
Broadcast News Analysts 84,830
Brokerage Clerks 43,690
Budget Analysts 73,650
Business and Financial Operations Occupations 66,890
Business Operations Specialists, All Other 77,280
Business Teachers, Postsecondary 78,240
Buyers and Purchasing Agents, Farm Products 63,490
Camera and Photographic Equipment Repairers 41,910
Captains, Mates, and Pilots of Water Vessels 69,080
Cardiovascular Technologists and Technicians 44,690
Career/Technical Education Teachers, Middle School 53,190
Career/Technical Education Teachers, Secondary School 53,480
Cargo and Freight Agents 45,610
Cartographers and Photogrammetrists 54,170
Chefs and Head Cooks 45,090
Chemical Engineers 92,420
Chemical Equipment Operators and Tenders 52,430
Chemical Plant and System Operators 52,710
Chemical Technicians 43,370
Chemistry Teachers, Postsecondary 71,100
Chemists 70,740
Child, Family, and School Social Workers 40,580
Chiropractors 80,690
Civil Engineers 71,890
Claims Adjusters, Examiners, and Investigators 58,870
Clinical, Counseling, and School Psychologists 85,800
Coil Winders, Tapers, and Finishers 48,260
Commercial and Industrial Designers 48,120
Commercial Pilots 83,940
Communications Equipment Operators, All Other 40,600
Communications Teachers, Postsecondary 64,250
Community and Social Service Occupations 41,400
Community Health Workers 42,490
Compensation and Benefits Managers 87,210
Compensation, Benefits, and Job Analysis Specialists 56,600
Compliance Officers 62,600
Computer and Information Research Scientists 103,900
Computer and Information Systems Managers 119,170
Computer and Mathematical Occupations 73,780
Computer Hardware Engineers 99,980
Computer Network Architects 88,400
Computer Network Support Specialists 55,990
Computer Occupations, All Other 83,170
Computer Programmers 80,490
Computer Science Teachers, Postsecondary 91,360
Computer Systems Analysts 79,200
Computer User Support Specialists 45,150
Conservation Scientists 71,400
Construction and Building Inspectors 49,630
Construction Managers 89,680
Continuous Mining Machine Operators 42,760
Control and Valve Installers and Repairers, Except Mechanical Door 41,050
Conveyor Operators and Tenders 40,400
Cost Estimators 56,980
Crane and Tower Operators 43,910
Credit Analysts 50,290
Credit Counselors 43,360
Criminal Justice and Law Enforcement Teachers, Postsecondary 57,230
Curators 48,470
Database Administrators 70,120
Dental Hygienists 46,530
Derrick Operators, Oil and Gas 44,610
Detectives and Criminal Investigators 57,820
Diagnostic Medical Sonographers 47,760
Dietitians and Nutritionists 46,720
Directors, Religious Activities and Education 41,590
Drafters, All Other 48,090
Economics Teachers, Postsecondary 96,290
Economists 104,280
Editors 46,760
Education Administrators, All Other 81,870
Education Administrators, Elementary and Secondary School 77,880
Education Administrators, Postsecondary 95,040
Education Administrators, Preschool and Childcare Center/Program 61,290
Education Teachers, Postsecondary 57,390
Education, Training, and Library Occupations 45,000
Educational, Guidance, School, and Vocational Counselors 50,820
Electric Motor, Power Tool, and Related Repairers 41,380
Electrical and Electronics Drafters 61,360
Electrical and Electronics Engineering Technicians 56,160
Electrical and Electronics Installers and Repairers, Transportation Equipment 52,450
Electrical and Electronics Repairers, Commercial and Industrial Equipment 52,650
Electrical and Electronics Repairers, Powerhouse, Substation, and Relay 63,870
Electrical Engineers 91,040
Electrical Power-Line Installers and Repairers 59,730
Electricians 43,200
Electro-Mechanical Technicians 49,150
Electronics Engineers, Except Computer 100,310
Elementary School Teachers, Except Special Education 48,970
Elevator Installers and Repairers 67,930
Embalmers 46,100
Emergency Management Directors 67,970
Engineering Technicians, Except Drafters, All Other 62,320
English Language and Literature Teachers, Postsecondary 52,330
Environmental Engineering Technicians 48,520
Environmental Engineers 69,970
Environmental Science and Protection Technicians, Including Health 42,510
Environmental Science Teachers, Postsecondary 78,700
Environmental Scientists and Specialists, Including Health 58,640
Epidemiologists 59,130
Executive Secretaries and Executive Administrative Assistants 52,530
Exercise Physiologists 43,150
Explosives Workers, Ordnance Handling Experts, and Blasters 49,580
Extruding, Forming, Pressing, and Compacting Machine Setters, Operators, and Tenders 41,190
Farm and Home Management Advisors 49,430
Film and Video Editors 43,940
Financial Analysts 93,970
Financial Clerks, All Other 42,830
Financial Examiners 78,040
Financial Managers 116,110
Financial Specialists, All Other 67,910
Fire Inspectors and Investigators 47,100
Firefighters 40,590
First-Line Supervisors of Construction Trades and Extraction Workers 55,990
First-Line Supervisors of Correctional Officers 53,470
First-Line Supervisors of Farming, Fishing, and Forestry Workers 46,170
First-Line Supervisors of Fire Fighting and Prevention Workers 57,160
First-Line Supervisors of Helpers, Laborers, and Material Movers, Hand 44,310
First-Line Supervisors of Landscaping, Lawn Service, and Groundskeeping Workers 40,300
First-Line Supervisors of Mechanics, Installers, and Repairers 59,010
First-Line Supervisors of Non-Retail Sales Workers 74,600
First-Line Supervisors of Office and Administrative Support Workers 49,740
First-Line Supervisors of Police and Detectives 62,800
First-Line Supervisors of Production and Operating Workers 55,630
First-Line Supervisors of Protective Service Workers, All Other 44,570
First-Line Supervisors of Transportation and Material-Moving Machine and Vehicle Operators 52,950
Fish and Game Wardens 46,110
Food Service Managers 59,820
Foreign Language and Literature Teachers, Postsecondary 55,340
Forensic Science Technicians 41,700
Forest and Conservation Technicians 43,210
Foresters 56,020
Forestry and Conservation Science Teachers, Postsecondary 90,080
Fundraisers 51,930
Funeral Service Managers 53,210
Gaming Supervisors 43,260
Gas Compressor and Gas Pumping Station Operators 56,220
Gas Plant Operators 61,780
General and Operations Managers 119,850
Geography Teachers, Postsecondary 67,430
Geological and Petroleum Technicians 58,700
Geoscientists, Except Hydrologists and Geographers 71,260
Health and Safety Engineers, Except Mining Safety Engineers and Inspectors 88,670
Health Diagnosing and Treating Practitioners, All Other 56,990
Health Educators 44,920
Health Specialties Teachers, Postsecondary 108,160
Health Technologists and Technicians, All Other 43,140
Healthcare Practitioners and Technical Occupations 63,080
Healthcare Social Workers 44,080
Hearing Aid Specialists 42,170
Historians 62,210
History Teachers, Postsecondary 56,050
Hoist and Winch Operators 54,330
Home Economics Teachers, Postsecondary 71,420
Human Resources Managers 93,630
Human Resources Specialists 58,160
Industrial Engineering Technicians 57,510
Industrial Engineers 81,330
Industrial Machinery Mechanics 48,790
Industrial Production Managers 93,500
Information and Record Clerks, All Other 41,230
Information Security Analysts 78,810
Installation, Maintenance, and Repair Occupations 42,340
Instructional Coordinators 65,060
Insurance Appraisers, Auto Damage 75,530
Insurance Sales Agents 54,050
Insurance Underwriters 52,330
Interior Designers 46,540
Judges, Magistrate Judges, and Magistrates 58,140
Kindergarten Teachers, Except Special Education 47,990
Labor Relations Specialists 50,100
Landscape Architects 72,760
Lawyers 106,790
Layout Workers, Metal and Plastic 47,290
Legal Occupations 81,140
Legal Support Workers, All Other 51,570
Librarians 52,340
Library Science Teachers, Postsecondary 60,360
Life Scientists, All Other 55,510
Life, Physical, and Social Science Occupations 58,420
Loading Machine Operators, Underground Mining 41,270
Loan Officers 67,070
Locomotive Engineers 55,900
Logging Workers, All Other 41,940
Logisticians 81,280
Magnetic Resonance Imaging Technologists 55,430
Management Analysts 90,310
Managers, All Other 94,950
Marine Engineers and Naval Architects 57,230
Market Research Analysts and Marketing Specialists 58,340
Marketing Managers 111,320
Marriage and Family Therapists 43,780
Materials Engineers 95,030
Mathematical Science Teachers, Postsecondary 62,740
Mechanical Drafters 52,840
Mechanical Engineering Technicians 51,900
Mechanical Engineers 83,370
Media and Communication Equipment Workers, All Other 66,370
Medical and Clinical Laboratory Technologists 52,900
Medical and Health Services Managers 93,750
Medical Equipment Repairers 44,240
Meeting, Convention, and Event Planners 45,020
Mental Health Counselors 42,720
Metal-Refining Furnace Operators and Tenders 44,330
Middle School Teachers, Except Special and Career/Technical Education 48,830
Millwrights 43,300
Mine Cutting and Channeling Machine Operators 46,410
Mine Shuttle Car Operators 53,150
Mining and Geological Engineers, Including Mining Safety Engineers 81,970
Mining Machine Operators, All Other 45,660
Mixing and Blending Machine Setters, Operators, and Tenders 40,740
Mobile Heavy Equipment Mechanics, Except Engines 43,340
Model Makers, Metal and Plastic 41,780
Morticians, Undertakers, and Funeral Directors 40,170
Multimedia Artists and Animators 57,700
Music Directors and Composers 48,190
Natural Sciences Managers 113,650
Network and Computer Systems Administrators 68,990
Nuclear Engineers 110,620
Nuclear Medicine Technologists 55,820
Nuclear Technicians 59,630
Nurse Practitioners 88,320
Nursing Instructors and Teachers, Postsecondary 66,660
Occupational Health and Safety Specialists 66,150
Occupational Health and Safety Technicians 49,620
Occupational Therapists 73,260
Occupational Therapy Assistants 55,190
Operations Research Analysts 87,680
Optometrists 96,210
Orthotists and Prosthetists 62,630
Painters, Transportation Equipment 41,180
Paper Goods Machine Setters, Operators, and Tenders 41,360
Paralegals and Legal Assistants 45,510
Patternmakers, Metal and Plastic 40,310
Personal Financial Advisors 101,700
Petroleum Pump System Operators, Refinery Operators, and Gaugers 54,140
Pharmacists 119,020
Philosophy and Religion Teachers, Postsecondary 61,760
Physical Therapist Assistants 53,710
Physical Therapists 83,460
Physician Assistants 88,680
Physicists 108,740
Physics Teachers, Postsecondary 78,630
Plant and System Operators, All Other 67,440
Plumbers, Pipefitters, and Steamfitters 40,170
Podiatrists 112,230
Police and Sheriff’s Patrol Officers 41,040
Political Science Teachers, Postsecondary 66,490
Postal Service Clerks 45,400
Postal Service Mail Carriers 49,350
Postal Service Mail Sorters, Processors, and Processing Machine Operators 48,360
Postmasters and Mail Superintendents 68,750
Power Distributors and Dispatchers 70,530
Power Plant Operators 60,720
Precision Instrument and Equipment Repairers, All Other 46,990
Private Detectives and Investigators 57,620
Probation Officers and Correctional Treatment Specialists 43,000
Producers and Directors 50,920
Production, Planning, and Expediting Clerks 46,020
Property, Real Estate, and Community Association Managers 67,390
Psychologists, All Other 86,080
Psychology Teachers, Postsecondary 68,910
Public Relations and Fundraising Managers 89,080
Public Relations Specialists 47,070
Pump Operators, Except Wellhead Pumpers 41,850
Purchasing Agents, Except Wholesale, Retail, and Farm Products 63,950
Purchasing Managers 104,300
Radiation Therapists 68,470
Radio, Cellular, and Tower Equipment Installers and Repairers 45,510
Radiologic Technologists 45,460
Rail Yard Engineers, Dinkey Operators, and Hostlers 49,580
Railroad Conductors and Yardmasters 52,200
Rail-Track Laying and Maintenance Equipment Operators 46,320
Real Estate Brokers 70,520
Real Estate Sales Agents 56,600
Recreation and Fitness Studies Teachers, Postsecondary 61,300
Recreational Vehicle Service Technicians 42,230
Refractory Materials Repairers, Except Brickmasons 47,440
Registered Nurses 55,870
Reinforcing Iron and Rebar Workers 40,590
Respiratory Therapists 46,200
Rolling Machine Setters, Operators, and Tenders, Metal and Plastic 41,290
Roof Bolters, Mining 54,150
Rotary Drill Operators, Oil and Gas 41,470
Sales Engineers 99,260
Sales Managers 111,910
Sales Representatives, Services, All Other 48,230
Sales Representatives, Wholesale and Manufacturing, Except Technical and Scientific Products 63,400
Sales Representatives, Wholesale and Manufacturing, Technical and Scientific Products 79,450
Secondary School Teachers, Except Special and Career/Technical Education 50,170
Securities, Commodities, and Financial Services Sales Agents 82,560
Service Unit Operators, Oil, Gas, and Mining 48,010
Set and Exhibit Designers 54,620
Ship Engineers 69,300
Signal and Track Switch Repairers 52,340
Social and Community Service Managers 61,440
Social Scientists and Related Workers, All Other 80,010
Social Work Teachers, Postsecondary 67,040
Social Workers, All Other 60,040
Sociology Teachers, Postsecondary 59,760
Software Developers, Applications 91,070
Software Developers, Systems Software 96,290
Soil and Plant Scientists 60,470
Sound Engineering Technicians 41,870
Special Education Teachers, All Other 55,310
Special Education Teachers, Kindergarten and Elementary School 50,810
Special Education Teachers, Middle School 52,200
Special Education Teachers, Secondary School 52,390
Speech-Language Pathologists 65,140
Stationary Engineers and Boiler Operators 46,730
Statisticians 58,210
Surveyors 51,410
Tank Car, Truck, and Ship Loaders 48,810
Tax Examiners and Collectors, and Revenue Agents 53,860
Technical Writers 59,590
Telecommunications Equipment Installers and Repairers, Except Line Installers 50,940
Tire Builders 42,500
Tool and Die Makers 46,750
Training and Development Managers 87,630
Training and Development Specialists 57,180
Transportation Inspectors 65,650
Transportation, Storage, and Distribution Managers 86,090
Urban and Regional Planners 58,590
Veterinarians 79,820
Water and Wastewater Treatment Plant and System Operators 42,750
Web Developers 50,610
Wholesale and Retail Buyers, Except Farm Products 55,700
Writers and Authors 54,250
Zoologists and Wildlife Biologists 59,000

Sheet2

Sheet3

Statistics homework help

RUBRIC

Criterion 1

A – 4 – Mastery

Submission skillfully includes: an introduction, a matrix table, a conclusion, three recommendations

Criterion 2

A – 4 – Mastery

Submission skillfully includes a matrix table of the three data visualization tools whose pertinent features closely match the needs of the firm.

Criterion 3

A – 4 – Mastery

Thorough rating of ease of learning and use of the tool.

Criterion 4

A – 4 – Mastery

Thorough presentation of cost information including subscription and maintenance fees.

Criterion 5

A – 4 – Mastery

Thorough ranking of products including a single final recommendation

Statistics homework help

Unit 4: Report Writing
Research Report

THE CHANGE IN THE AUSTRALIAN WORK FORCE SINCE THE
END OF WORLD WAR II

Prepared by: NAME SURNAME

Preparation for Tertiary Studies Course
Victorian University of Technology

Lecturer: NAME SURNAME

2nd September 2001

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Summary

This report discusses the changes that have occurred in the Australian workforce since
the end of World War II (1945-2000). A review of some of the available literature
provides insights into the changing role of women and migrants in the workforce, and the
influence of new technologies and changing levels of unemployment have also been
considered.

Key findings include:

There has been a marked increase in women’s participation in the workforce,
particularly that of married women.

While immigration was encouraged in post-war Australia as a way of providing
labour for new industries and major projects, the migrant population continues to
experience a high rate of unemployment in low-skilled jobs.

During the period 1945-2000, the nature of work in Australia has changed with a shift
from labour-intensive rural and manufacturing industries to ‘white collar’ industries
like tourism and entertainment.

The number and proportion of unemployed people in Australia has risen dramatically,
and factors that influence a person’s likelihood of experiencing unemployment
include age, proficiency in speaking English, and geographic location.

The information presented in this report has been gathered from secondary sources, and
from Australian Bureau of Statistics’ data.

The report has been prepared for submission as Unit 4 of the Tertiary Studies Course at
Victoria University.

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TABLE OF CONTENTS

Summary 2

1 Introduction 4

2 Findings 5

2.1 Women’s Workforce Participation Rate
Table 1. Proportion of women in the manufacturing industry 5

2.2 Migrant Workers’ Participation Rates 6
2.3 Employment Categories 7
2.4 Unemployment and Demographic Factors 8

3 Conclusion 10

4 Recommendation 10

5 Reference List 11

6 Appendix A: Employment by Industry, 1970-1995 12

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1 Introduction

The profile of the Australian workforce has a ltered markedly since the end of World War
II. Australia has transform ed from a nation of predom inantly Anglo-Celtic cultu re and
almost full em ployment to one of rich cultural diversity with relatively high
unemployment. This report exam ines ways in which our workforce has changed,
focusing on the f ollowing categories: women’s workforce participation rates, m igrant
workers’ participation rates, e mployment categories, unemployment rates and
demographic profiles. This repor t will also consider n ew influences affecting the
workforce.

This report is an assessable com ponent of th e Preparation for Tertiary Studies course at
Victoria University of Technology, Werribee Campus.

1.1 Methodology

Information for this report was sourced from various secondary sources, all listed in the
Reference List. Data from publications by the Australian Bureau of Statistics also proved
valuable. This report is not a comprehensiv e review of the ava ilable literature, but
provides a broad overview of the topic.

1.2 Scope of the report

Wherever the term ‘workforce’ on its own is u sed, it is in reference to the Austr alian
workforce. Where the infor mation refers to a particular state, th is will be noted. The
period under consideration is 1945 to 2000, alt hough where available data does not cover
the entire period, this is stated. The re port focuses on several key aspects of the
Australian workforce, and is not a com prehensive account of al l changes that have
occurred in the workforce since World War II.

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Concurrent Study Research Report Page 4

2. Findings

2.1 Women’s Workforce Participation Rates

The overall participation rate of women in the Australian workforce since the end
of World War II has in creased markedly. The absence of m ale workers during the
war ‘brought into the workforce considerable numbers of women who had not been
employed before the war broke out’ (Ryan and Conlon 1989, p. 137). However,
many women gave up their jobs when the men returned. Their rates of pay
compared to men were reduced in th e post-war years (R yan and Conlon 1989, pp.
140-144). Edna Ryan and Anne Conlon provi de the following table, which shows
that the proportion of wom en in the manufacturing industry peaked during the war,
declined until 1959, and then began to increase gradually.

Table 1. Proportion of women in the manufacturing industry.

Males to every
100 females

1932-3 239
1938-9 271
1943-4 237
1944-5 250
1947-8 308
1951-2 315
1954-5 325
1957-8 327
1958-9 330
1961-2 326
1962-3 319

Over the next 29 years, cam paigns for equal pay (or at leas t for better than 75 per
cent of the male rate for the same work) took place across many industries, and this
was achieved in principle in 1974 (Ryan and Conlon 1989, ch. 6).

In 1945, 24 per cent of the workforce in Australia was women (Zajdow 1995, p. 3).
By 1947, this had dropped back to 22.4 per cent. In 1973, this had increased to 33
per cent (Ryan and Conlon 1989, p. 174). In 1993, wom en made up 52 per cent of
the workforce (Zajdow 1995, p. 3).

The increase in married women in the workforce has been particularly marked.

‘In 1947 only 15.3 per cent of wom en in the female labour force were
married, or 3.4 per cent of the tota l labour force. In 1971 56.8 per cent
of women in the fem ale labour force were m arried, or 18 per cent of
the total labour force.’ (Ryan and Conlon 1989, p. 174)

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Married women’s participation increased ra pidly after 1971. This is due, in part, to
the fact that until the 1950s, women in government employment, including teachers
and university staff, had been required to leave their jobs upon m arrying. In 1971,
36 per cent of all m arried women were in paid work. In 1995, 55 per cent of all
married women were in paid work. During this time, the proportion of men in paid
work declined by 10 per cen t, and the proportion of un married women has stayed
the same (Norris and Wooden 1996, p. 2).

Much of the growth in wom en’s employment has occurred as wom en have moved
from the ‘feminine’ careers of teaching a nd nursing into resp ectable ‘white collar’
industries such as banking and retailing (Game and Pringle 1983, p. 19).

Participation in the work force is uneven across different groups of wom en such as
sole parents and Aboriginal and Torres St rait Islanders who have lower rates of
participation. However, the particip ation rate of wom en in ge neral is higher now
than at the conclusion of World War II (Zajdow 1995, p3; Ryan and Conlon 1989,
p. 174).

2.2 Migrant Workers’ Participation Rates

The years since the end of the S econd World War have seen an increase in
immigration into Austra lia and the refore an incr ease in the num ber of migrants in
the workforce. Post-war Australia saw th e rapid national developm ent of projects
such as the Snowy Mountains Hydro-Electric Scheme. This meant a great dem and
for labour, which the Australian workforce could not fulfil at the tim e. Migrants
were therefore encouraged to come to Australia to f ill such jobs, res ulting in a
period of high migrant employment (Carroll 1989, p. 48).

Workers born overseas now constitute a s ubstantial proportion of the workforce;
however, this group does suffer a high une mployment rate. Some of the reasons for
this include their lack of proficiency in English, the undervaluing or lack of
recognition of qualifications received overseas, the lack of a verifiable employment
‘history’ with which to impress employers, discrimination and under-representation
in trade unions (VandenHeuvel and Wooden 1996, pp. 7-8). All of these factors are
more pronounced among non-English speaking background (NESB) women.

‘Prior to the 1980s, the convent ional wisdom was that NESB
immigrants, including wom en, had higher rates of labour force
participation than their Australia- born counterparts… By the early
1980s, however, this situation had dr amatically altered, such that
labour force participation rates of both NESB men and women now lie
well below that of Australia-born men and wom en.’ (VandenHeuvel
and Wooden 1996, p. 10)

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The large increase in married women in the workforce applies only to Austra lia-
born women (a 14 per cent increase from 1980-94), and English-speaking
background (ESB) m igrants (a 9.7 per cen t increase). The proportion of m arried,
NESB migrant women in the labour force dropped slightly over the period
(VandenHeuvel and Wooden 1996, p. 10). Wo rkforce participation for NESB
women varies depending on their country of origin, but overall, their participation
has decreased (VandenHeuvel and Wooden 1996, p. 11).

Unemployment rates for NESB women show that in 1980 there was little difference
from the unemployment rate of 7-8 per cent for women regardless of their country
of birth (including Australia). By 1994, fi gures for Australia-born and ESB wom en
were still at that level, while the ra te for NESB women had peaked at o ver 16 per
cent in 1993 before falling to 15 per cent (VandenHeuvel and Wooden 1996, p. 15).

Post-war Australia saw a dramatic increa se in immigration; however, the migrant
population does experience a high degree of unemployment and participation in
lower-skilled jobs compared to people born in Australia.

2.3 Employment Categories

The major types of employm ent dominating the workforce at th e conclusion of
World War Two differ greatly from the categories of employm ent available in
recent times. After 1945, the Governm ent encouraged m anufacturing. This was
initially to provide employment for returned servicemen, then later to lower imports
as a m eans to ease its balance o f payment difficulties. Rural ind ustries also
prospered at this tim e due to a short supply of food and basic commodities in
countries badly ravaged by the war. By 1950, 28 per cent of Australians were
employed in secondary industries and 17 per cent in prim ary industries (Carroll
1989, p48). The proportion of Australians employed in these areas has since fallen.

In the early 1970s, the governm ent reduced tariffs for pri mary exports in an effort
to enter into trade agreem ents with Asian countries. This w as followed soon after
by a recession, and th e markets that the gov ernment had hoped to reach with their
manufactured goods dried up. Australian ru ral and m ining industries also suffered
and this reduced em ployee numbers. In the early 1980s, a severe drought and
another economic slump once again reduced employment opportunities in prim ary
industries (Carroll 1989, p56).

From 1970 to 1995, the percentage of the to tal workforce engaged in agriculture
and mining dropped from 9.6 per cent to 6 per cent. The proportion of the
workforce engaged in m anufacturing dropped from 24.5 per cent to 13.6 per cent.
The services industry, including occupati ons like hairdressing, entertainment,
hospitality and tourism , has seen signif icant growth during the sam e period. The
proportion of the workforce engaged in services has increased from 47.8 per cent to
65.7 per cent. (Norris and W ooden 1996, p. 6). See Appendix A for a fi ve-yearly
breakdown of these shifts.

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As the end of the cen tury drew closer, entirely new types of employment emerged
and are still growing. Many labour-intensive industrial jobs are now automated and
performed by com puters, microprocessors or robots. Inform ation technology is
quickly becoming a growing area of em ployment in Austra lia with m any jobs
centred around the selling, servicing, pr ogramming and operating of com puters
(Carroll 1989, p. 56).

The Australian workforce has gone from being largely based around manufacturing
and exporting to being largely based around importing and consumerism.

2.4 Unemployment and Demographic Rates

Australia has experienced a dram atic increase in the rate o f unemployment since
the end of World W ar Two. At that tim e, and for approxim ately the next thirty
years, unemployment was virtually non-exis tent and work was readily available
(Carroll 1989, p. 48). In 1970, the unem ployment rate was 1.5 per cent of the
labour force, and the underem ployment rate was less than 1 per cent (N orris and
Wooden 1996, p. 8). U nderemployment is defined as part-tim e workers who would
prefer to work m ore hours and full-tim e workers who worked less than their usual
hours for economic reasons.

This is in contrast to current tr ends. Between 1970 and 1995, underemploym ent
rose fairly steadily to 7 per cent of the total labour force, while unemployment rose
in three dramatic jumps in the m id-1970s (to 4 per cent), the early 1980s (to 9 pe r
cent) and the early 1990s (to 10 per cent). The late 1980s saw the unemploym ent
rate drop back to less than 6 per cent and, after peaking again at over 10 per cent in
the interim, in 1998, the unem ployment rate had fallen to eight percent (Australian
Bureau of Statistics 1999; Norris and Wooden 1996, p. 8). It is not uncommon for
job seekers to be without em ployment for several years at a tim e. In 1994, 35 per
cent of unemployed people had experienced long-term unemployment. This rate
has decreased since that tim e (Norris and Wooden 1996, p. 9). A range of
demographic factors and indicators affects the current high rate of unemployment.

Several factors determ ine a person’s likel ihood of experiencing unem ployment in
the current working clim ate. These in clude socio-economic background, area of
residence (rural versus urban areas), prof iciency in speaking English, age, and to a
lesser degree, sex.

The following data was obtained by the Au stralian Bureau of Statistics in
September 1997, and pertains to job seekers nation wide. At this tim e, an average
of twenty-seven percent of job seekers from the lowest socio-economic background
had not worked at all, com pared to seventeen p ercent of those from higher socio-
economic areas. The proportion of job seek ers that had not worked since May 1995
was highest in m ajor urban areas (27 per cent) and lowest in rural areas (20 pe r
cent). There is also a solid link betw een a person’s lack of prof iciency in speaking

Version 1.0
Concurrent Study Research Report Page 8

English and unem ployment. Sixty one per cent of persons who do not speak
English proficiently or at all had been unemployed since 1995. It also appears that
the older a person is, the greater the chan ce of being unem ployed for a long period
of time. Forty three per cent of job seekers between the ag es of forty-five to fifty-
nine had not worked since May 1995. Fifty per cent of these people reported that
they were considered to be too old by employers. Virtually the same proportions of
male and fe male job seekers were in stable em ployment at Septem ber 1997. The
only variation was that f or males, this work was predominantly full-time, while for
females, half were working part-time (Australian Bureau of Statistics 1997, p. 20).

In a period of fifty-five years, Australian has tr ansformed from a nation of
practically no unemployment to one of reasonably high unemployment with rather
complex and varied causes.

Version 1.0
Concurrent Study Research Report Page 9

3. Conclusion

The Australian workforce has altered greatly in the fifty-five years since the end of World
War II. Many of these changes have been very positive, such as the growth of women in
the workforce, the formation of many new employment categories and the introduction of
migration to cope with a tim e of great industr ial growth, which has in turn enriched our
culture.

There are, however, som e negative aspects associated with the transf ormation. Many
areas of employment have been replaced by m achinery or other technologies, displacing
unskilled workers. Consequently, Australian society is now experiencing a high dem and
for a skilled labour force, and an increasing se ctor of the population without such skills is
suffering long-term unemployment. The change experienced in such a relatively short
period of time leads to the question: what do the next fifty-five years hold?

4. Recommendation

The information collected for this report provides a broad overview of key changes in the
Australian workforce. Further analysis would be possible if the relevant data for each
year from 1945-2000 was purchased from the Australian Bureau of Statistics. The
reliance on secondary sources has resulted in some patchy data. For example, it is not
possible to identify for any given year a breakdown of the Australian workforce by the
following categories:

• unmarried Australia-born women
• married Australia-born women
• unmarried Australia-born men
• married Australia-born men
• unmarried immigrant women
• married immigrant women
• unmarried immigrant men
• married immigrant men

Greater access to primary data would enable a more thorough analysis to be made.

Version 1.0
Concurrent Study Research Report Page 10

5. Reference List

Australian Bureau of Statistics 1997, Australians, Employment and Unemployment
Patterns: 1994-1997, ABS, Canberra.

Australian Bureau of Statistics 1999, Year Book Australia 1998, ABS, Canberra.

Carroll, B. 1989, Australians at Work through 200 Years, Kangaroo Press, Sydney.

Game, A. and Pringle, R. 1983, Gender at Work, George Allen & Unwin Australia Pt y
Ltd, North Sydney.

Norris, K. and W ooden, M. (eds.) 1996, The Changing Australian Labour Market,
Economic Planning Ad visory Committee, Australian Governm ent Publishing Service,
Canberra.

Ryan, E. and Conlon, A. 1989 (1975), Gentle Invaders: Australian Women at Work,
Penguin Books Australia, Ringwood.

VandenHeuvel, A. and Wooden, M. 1996, Non-English-speaking-background immigrant
women and part-time work, Bureau of I mmigration, Multicultural and Population
Research, Carlton South.

Victorian Ethnic Affairs Comm ission 1984, Migrants and the Workforce, VEAC,
Melbourne.

Zajdow, G. 1995, Women and Work – Current Issues and Debates, Deakin University
Press, Geelong.

Version 1.0
Concurrent Study Research Report Page 11

6. Appendix

Appendix A: Employment by Industry, 1970-1995 (% of total employment)

1970 1975 1980 1985 1990 1995
Agriculture and
mining

9.6 8.2 7.8 7.7 6.6 6.0

Manufacturing 24.5 21.6 19.7 16.7 15.3 13.6
Utilities,
construction,
transport &
communication

18.1 18.3 17.2 17.1 15.8 14.7

Services 47.8 52.0 55.4 58.6 62.3 65.7

Table from Norris and Wooden 1996, p. 6.

Version 1.0
Concurrent Study Research Report Page 12

  • Research Report
    • Summary
    • TABLE OF CONTENTS
      • Summary 2
      • 1 Introduction 4
        • 3 Conclusion 10
        • 4 Recommendation 10
          • 1.2 Scope of the report
            • Appendix A: Employment by Industry, 1970-1995 (% of total employment)

Statistics homework help

As a professional in the real world, you will need to research and understand various aspects of Business applications. Basic statistical analysis can be used to gain an understanding of current problems. This course project will assist you in applying basic statistical principles to a fictional scenario in order to impact the clients being served.

A major client of your company is interested in the salary distributions of jobs in the state of Georgia that range from $40,000 to $120,000 per year. As a Business Analyst your boss asks you to research and analyze the salary distributions. You are given a spreadsheet that contains the following information:

· A listing of the jobs by title

· The salary (in dollars) for each job

The client needs the preliminary findings by the end of the day. So let’s get to work!!!!

The data set consists of 364 records that you will be analyzing from the Bureau of Labor Statistics. The data set contains a listing of several jobs titles with yearly salaries ranging from approximately $40,000 to $120,000 for the state of Georgia.

Statistics homework help

Research Articles

Research Articles – Main Parts

Abstract

Introduction

Methods

Results

Discussion

References

Research Article – Main Parts

Abstract

Provides a brief overview of the article

Introduction

Discusses previous research that led the authors to their current study and research question(s) and hypothesis(ses)

Methods

Describes the sample/participants, outlines the tests used in the study and what each was used to measure/assess

Results

Will include both written and visual demonstrations (e.g., tables, graphs, figures) of results of the statistical analyses that were conducted

Discussion

Provides a summary of results, what were the important findings/why the study was important, and conclusions/future directions

References

Lists all the references that were cited throughout the article

Where is the Purpose/ Hypotheses?

The purpose will sometimes be labeled as “Purpose” or “Objective” in the abstract

The purpose(s) and hypothesis(ses) can also be found at the END (typically the last paragraph) of the Introduction section

Lange, E., Kucharski, D., Svedlund, S., Svensson, K., Bertholds, G., Gjertsson, I., & Mannerkorpi, K. (2019). Effects of aerobic and resistance exercise in older adults with rheumatoid arthritis: a randomized controlled trial. Arthritis Care & Research, 71(1), 61-70.

4

How to tell is they are looking at differences/ relationships/or both

One, you can look at the wording of their hypotheses and what kinds of variables they are using

Two, it can also be helpful to look at which statistical analyses they used

Remember we learned in class that there are some statistical analyses that only look at differences and some that only look at relationships

And, for instance, if they used t-tests and regressions then we know they looked at BOTH differences and relationships

What types of variables did they use?

To identify their variables, you can look at their:

Hypotheses

Visual displays of the data (e.g., tables, graphs, figures)

It can be helpful to look at their tables/graphs if you are having trouble identifying which scale of measurement is used for their variables

If there are different groups in their tables/ x-axis of their graph – then we know it is a categorial variable

Tables and graphs will also show values – whether those values/numbers in the table/graph are all positive, or if they can be negative will help you determine which scale of measurement is being used as well.

Where do I find the tests they used?

Methods Section

The tests, or the tools/instruments, that were given to participants will be outlined in the Methods section

The tests are what the researchers gave participants/ what they had the participants DO in the study

In the example article to the left, what test was used?

One test used was the “Youth Sport Environment Questionnaire”

What did it measure?

It measured perceptions of task cohesion

Spink, K. S., McLaren, C. D., & Ulvick, J. D. (2018). Groupness, cohesion, and intention to return to sport: A study of intact youth teams. International Journal of Sports Science & Coaching, 13(4), 545-551.

7

Where do I find the Statistical Analyses

The statistical analyses section is typically:

At the end of the methods section

OR

Beginning of the results section

Sometimes the section is clearly labeled as “Statistical Analyses” or “Data Analyses”

Spink, K. S., McLaren, C. D., & Ulvick, J. D. (2018). Groupness, cohesion, and intention to return to sport: A study of intact youth teams. International Journal of Sports Science & Coaching, 13(4), 545-551.

8

Statistics homework help

Sheet1

Job Title Salary
Accountants and Auditors 63,910 source: http://www.bls.gov/
Actuaries 84,190
Administrative Law Judges, Adjudicators, and Hearing Officers 117,110
Administrative Services Managers 94,450
Adult Basic and Secondary Education and Literacy Teachers and Instructors 43,500
Advertising and Promotions Managers 75,710
Advertising Sales Agents 46,100
Aerospace Engineering and Operations Technicians 59,800
Aerospace Engineers 104,730
Agents and Business Managers of Artists, Performers, and Athletes 77,690
Agricultural and Food Science Technicians 44,470
Agricultural Inspectors 43,470
Agricultural Sciences Teachers, Postsecondary 92,010
Air Traffic Controllers 94,030
Aircraft Cargo Handling Supervisors 44,890
Aircraft Structure, Surfaces, Rigging, and Systems Assemblers 42,410
Airfield Operations Specialists 52,740
Airline Pilots, Copilots, and Flight Engineers 98,480
Anthropologists and Archeologists 43,970
Appraisers and Assessors of Real Estate 50,150
Arbitrators, Mediators, and Conciliators 56,700
Architects, Except Landscape and Naval 75,440
Architectural and Civil Drafters 46,470
Architecture and Engineering Occupations 79,910
Architecture Teachers, Postsecondary 79,040
Archivists 60,560
Art Directors 76,280
Art, Drama, and Music Teachers, Postsecondary 57,210
Athletic Trainers 42,330
Atmospheric and Space Scientists 84,390
Atmospheric, Earth, Marine, and Space Sciences Teachers, Postsecondary 92,630
Audiologists 53,830
Avionics Technicians 56,440
Biomedical Engineers 85,810
Boilermakers 55,870
Broadcast News Analysts 84,830
Brokerage Clerks 43,690
Budget Analysts 73,650
Business and Financial Operations Occupations 66,890
Business Operations Specialists, All Other 77,280
Business Teachers, Postsecondary 78,240
Buyers and Purchasing Agents, Farm Products 63,490
Camera and Photographic Equipment Repairers 41,910
Captains, Mates, and Pilots of Water Vessels 69,080
Cardiovascular Technologists and Technicians 44,690
Career/Technical Education Teachers, Middle School 53,190
Career/Technical Education Teachers, Secondary School 53,480
Cargo and Freight Agents 45,610
Cartographers and Photogrammetrists 54,170
Chefs and Head Cooks 45,090
Chemical Engineers 92,420
Chemical Equipment Operators and Tenders 52,430
Chemical Plant and System Operators 52,710
Chemical Technicians 43,370
Chemistry Teachers, Postsecondary 71,100
Chemists 70,740
Child, Family, and School Social Workers 40,580
Chiropractors 80,690
Civil Engineers 71,890
Claims Adjusters, Examiners, and Investigators 58,870
Clinical, Counseling, and School Psychologists 85,800
Coil Winders, Tapers, and Finishers 48,260
Commercial and Industrial Designers 48,120
Commercial Pilots 83,940
Communications Equipment Operators, All Other 40,600
Communications Teachers, Postsecondary 64,250
Community and Social Service Occupations 41,400
Community Health Workers 42,490
Compensation and Benefits Managers 87,210
Compensation, Benefits, and Job Analysis Specialists 56,600
Compliance Officers 62,600
Computer and Information Research Scientists 103,900
Computer and Information Systems Managers 119,170
Computer and Mathematical Occupations 73,780
Computer Hardware Engineers 99,980
Computer Network Architects 88,400
Computer Network Support Specialists 55,990
Computer Occupations, All Other 83,170
Computer Programmers 80,490
Computer Science Teachers, Postsecondary 91,360
Computer Systems Analysts 79,200
Computer User Support Specialists 45,150
Conservation Scientists 71,400
Construction and Building Inspectors 49,630
Construction Managers 89,680
Continuous Mining Machine Operators 42,760
Control and Valve Installers and Repairers, Except Mechanical Door 41,050
Conveyor Operators and Tenders 40,400
Cost Estimators 56,980
Crane and Tower Operators 43,910
Credit Analysts 50,290
Credit Counselors 43,360
Criminal Justice and Law Enforcement Teachers, Postsecondary 57,230
Curators 48,470
Database Administrators 70,120
Dental Hygienists 46,530
Derrick Operators, Oil and Gas 44,610
Detectives and Criminal Investigators 57,820
Diagnostic Medical Sonographers 47,760
Dietitians and Nutritionists 46,720
Directors, Religious Activities and Education 41,590
Drafters, All Other 48,090
Economics Teachers, Postsecondary 96,290
Economists 104,280
Editors 46,760
Education Administrators, All Other 81,870
Education Administrators, Elementary and Secondary School 77,880
Education Administrators, Postsecondary 95,040
Education Administrators, Preschool and Childcare Center/Program 61,290
Education Teachers, Postsecondary 57,390
Education, Training, and Library Occupations 45,000
Educational, Guidance, School, and Vocational Counselors 50,820
Electric Motor, Power Tool, and Related Repairers 41,380
Electrical and Electronics Drafters 61,360
Electrical and Electronics Engineering Technicians 56,160
Electrical and Electronics Installers and Repairers, Transportation Equipment 52,450
Electrical and Electronics Repairers, Commercial and Industrial Equipment 52,650
Electrical and Electronics Repairers, Powerhouse, Substation, and Relay 63,870
Electrical Engineers 91,040
Electrical Power-Line Installers and Repairers 59,730
Electricians 43,200
Electro-Mechanical Technicians 49,150
Electronics Engineers, Except Computer 100,310
Elementary School Teachers, Except Special Education 48,970
Elevator Installers and Repairers 67,930
Embalmers 46,100
Emergency Management Directors 67,970
Engineering Technicians, Except Drafters, All Other 62,320
English Language and Literature Teachers, Postsecondary 52,330
Environmental Engineering Technicians 48,520
Environmental Engineers 69,970
Environmental Science and Protection Technicians, Including Health 42,510
Environmental Science Teachers, Postsecondary 78,700
Environmental Scientists and Specialists, Including Health 58,640
Epidemiologists 59,130
Executive Secretaries and Executive Administrative Assistants 52,530
Exercise Physiologists 43,150
Explosives Workers, Ordnance Handling Experts, and Blasters 49,580
Extruding, Forming, Pressing, and Compacting Machine Setters, Operators, and Tenders 41,190
Farm and Home Management Advisors 49,430
Film and Video Editors 43,940
Financial Analysts 93,970
Financial Clerks, All Other 42,830
Financial Examiners 78,040
Financial Managers 116,110
Financial Specialists, All Other 67,910
Fire Inspectors and Investigators 47,100
Firefighters 40,590
First-Line Supervisors of Construction Trades and Extraction Workers 55,990
First-Line Supervisors of Correctional Officers 53,470
First-Line Supervisors of Farming, Fishing, and Forestry Workers 46,170
First-Line Supervisors of Fire Fighting and Prevention Workers 57,160
First-Line Supervisors of Helpers, Laborers, and Material Movers, Hand 44,310
First-Line Supervisors of Landscaping, Lawn Service, and Groundskeeping Workers 40,300
First-Line Supervisors of Mechanics, Installers, and Repairers 59,010
First-Line Supervisors of Non-Retail Sales Workers 74,600
First-Line Supervisors of Office and Administrative Support Workers 49,740
First-Line Supervisors of Police and Detectives 62,800
First-Line Supervisors of Production and Operating Workers 55,630
First-Line Supervisors of Protective Service Workers, All Other 44,570
First-Line Supervisors of Transportation and Material-Moving Machine and Vehicle Operators 52,950
Fish and Game Wardens 46,110
Food Service Managers 59,820
Foreign Language and Literature Teachers, Postsecondary 55,340
Forensic Science Technicians 41,700
Forest and Conservation Technicians 43,210
Foresters 56,020
Forestry and Conservation Science Teachers, Postsecondary 90,080
Fundraisers 51,930
Funeral Service Managers 53,210
Gaming Supervisors 43,260
Gas Compressor and Gas Pumping Station Operators 56,220
Gas Plant Operators 61,780
General and Operations Managers 119,850
Geography Teachers, Postsecondary 67,430
Geological and Petroleum Technicians 58,700
Geoscientists, Except Hydrologists and Geographers 71,260
Health and Safety Engineers, Except Mining Safety Engineers and Inspectors 88,670
Health Diagnosing and Treating Practitioners, All Other 56,990
Health Educators 44,920
Health Specialties Teachers, Postsecondary 108,160
Health Technologists and Technicians, All Other 43,140
Healthcare Practitioners and Technical Occupations 63,080
Healthcare Social Workers 44,080
Hearing Aid Specialists 42,170
Historians 62,210
History Teachers, Postsecondary 56,050
Hoist and Winch Operators 54,330
Home Economics Teachers, Postsecondary 71,420
Human Resources Managers 93,630
Human Resources Specialists 58,160
Industrial Engineering Technicians 57,510
Industrial Engineers 81,330
Industrial Machinery Mechanics 48,790
Industrial Production Managers 93,500
Information and Record Clerks, All Other 41,230
Information Security Analysts 78,810
Installation, Maintenance, and Repair Occupations 42,340
Instructional Coordinators 65,060
Insurance Appraisers, Auto Damage 75,530
Insurance Sales Agents 54,050
Insurance Underwriters 52,330
Interior Designers 46,540
Judges, Magistrate Judges, and Magistrates 58,140
Kindergarten Teachers, Except Special Education 47,990
Labor Relations Specialists 50,100
Landscape Architects 72,760
Lawyers 106,790
Layout Workers, Metal and Plastic 47,290
Legal Occupations 81,140
Legal Support Workers, All Other 51,570
Librarians 52,340
Library Science Teachers, Postsecondary 60,360
Life Scientists, All Other 55,510
Life, Physical, and Social Science Occupations 58,420
Loading Machine Operators, Underground Mining 41,270
Loan Officers 67,070
Locomotive Engineers 55,900
Logging Workers, All Other 41,940
Logisticians 81,280
Magnetic Resonance Imaging Technologists 55,430
Management Analysts 90,310
Managers, All Other 94,950
Marine Engineers and Naval Architects 57,230
Market Research Analysts and Marketing Specialists 58,340
Marketing Managers 111,320
Marriage and Family Therapists 43,780
Materials Engineers 95,030
Mathematical Science Teachers, Postsecondary 62,740
Mechanical Drafters 52,840
Mechanical Engineering Technicians 51,900
Mechanical Engineers 83,370
Media and Communication Equipment Workers, All Other 66,370
Medical and Clinical Laboratory Technologists 52,900
Medical and Health Services Managers 93,750
Medical Equipment Repairers 44,240
Meeting, Convention, and Event Planners 45,020
Mental Health Counselors 42,720
Metal-Refining Furnace Operators and Tenders 44,330
Middle School Teachers, Except Special and Career/Technical Education 48,830
Millwrights 43,300
Mine Cutting and Channeling Machine Operators 46,410
Mine Shuttle Car Operators 53,150
Mining and Geological Engineers, Including Mining Safety Engineers 81,970
Mining Machine Operators, All Other 45,660
Mixing and Blending Machine Setters, Operators, and Tenders 40,740
Mobile Heavy Equipment Mechanics, Except Engines 43,340
Model Makers, Metal and Plastic 41,780
Morticians, Undertakers, and Funeral Directors 40,170
Multimedia Artists and Animators 57,700
Music Directors and Composers 48,190
Natural Sciences Managers 113,650
Network and Computer Systems Administrators 68,990
Nuclear Engineers 110,620
Nuclear Medicine Technologists 55,820
Nuclear Technicians 59,630
Nurse Practitioners 88,320
Nursing Instructors and Teachers, Postsecondary 66,660
Occupational Health and Safety Specialists 66,150
Occupational Health and Safety Technicians 49,620
Occupational Therapists 73,260
Occupational Therapy Assistants 55,190
Operations Research Analysts 87,680
Optometrists 96,210
Orthotists and Prosthetists 62,630
Painters, Transportation Equipment 41,180
Paper Goods Machine Setters, Operators, and Tenders 41,360
Paralegals and Legal Assistants 45,510
Patternmakers, Metal and Plastic 40,310
Personal Financial Advisors 101,700
Petroleum Pump System Operators, Refinery Operators, and Gaugers 54,140
Pharmacists 119,020
Philosophy and Religion Teachers, Postsecondary 61,760
Physical Therapist Assistants 53,710
Physical Therapists 83,460
Physician Assistants 88,680
Physicists 108,740
Physics Teachers, Postsecondary 78,630
Plant and System Operators, All Other 67,440
Plumbers, Pipefitters, and Steamfitters 40,170
Podiatrists 112,230
Police and Sheriff’s Patrol Officers 41,040
Political Science Teachers, Postsecondary 66,490
Postal Service Clerks 45,400
Postal Service Mail Carriers 49,350
Postal Service Mail Sorters, Processors, and Processing Machine Operators 48,360
Postmasters and Mail Superintendents 68,750
Power Distributors and Dispatchers 70,530
Power Plant Operators 60,720
Precision Instrument and Equipment Repairers, All Other 46,990
Private Detectives and Investigators 57,620
Probation Officers and Correctional Treatment Specialists 43,000
Producers and Directors 50,920
Production, Planning, and Expediting Clerks 46,020
Property, Real Estate, and Community Association Managers 67,390
Psychologists, All Other 86,080
Psychology Teachers, Postsecondary 68,910
Public Relations and Fundraising Managers 89,080
Public Relations Specialists 47,070
Pump Operators, Except Wellhead Pumpers 41,850
Purchasing Agents, Except Wholesale, Retail, and Farm Products 63,950
Purchasing Managers 104,300
Radiation Therapists 68,470
Radio, Cellular, and Tower Equipment Installers and Repairers 45,510
Radiologic Technologists 45,460
Rail Yard Engineers, Dinkey Operators, and Hostlers 49,580
Railroad Conductors and Yardmasters 52,200
Rail-Track Laying and Maintenance Equipment Operators 46,320
Real Estate Brokers 70,520
Real Estate Sales Agents 56,600
Recreation and Fitness Studies Teachers, Postsecondary 61,300
Recreational Vehicle Service Technicians 42,230
Refractory Materials Repairers, Except Brickmasons 47,440
Registered Nurses 55,870
Reinforcing Iron and Rebar Workers 40,590
Respiratory Therapists 46,200
Rolling Machine Setters, Operators, and Tenders, Metal and Plastic 41,290
Roof Bolters, Mining 54,150
Rotary Drill Operators, Oil and Gas 41,470
Sales Engineers 99,260
Sales Managers 111,910
Sales Representatives, Services, All Other 48,230
Sales Representatives, Wholesale and Manufacturing, Except Technical and Scientific Products 63,400
Sales Representatives, Wholesale and Manufacturing, Technical and Scientific Products 79,450
Secondary School Teachers, Except Special and Career/Technical Education 50,170
Securities, Commodities, and Financial Services Sales Agents 82,560
Service Unit Operators, Oil, Gas, and Mining 48,010
Set and Exhibit Designers 54,620
Ship Engineers 69,300
Signal and Track Switch Repairers 52,340
Social and Community Service Managers 61,440
Social Scientists and Related Workers, All Other 80,010
Social Work Teachers, Postsecondary 67,040
Social Workers, All Other 60,040
Sociology Teachers, Postsecondary 59,760
Software Developers, Applications 91,070
Software Developers, Systems Software 96,290
Soil and Plant Scientists 60,470
Sound Engineering Technicians 41,870
Special Education Teachers, All Other 55,310
Special Education Teachers, Kindergarten and Elementary School 50,810
Special Education Teachers, Middle School 52,200
Special Education Teachers, Secondary School 52,390
Speech-Language Pathologists 65,140
Stationary Engineers and Boiler Operators 46,730
Statisticians 58,210
Surveyors 51,410
Tank Car, Truck, and Ship Loaders 48,810
Tax Examiners and Collectors, and Revenue Agents 53,860
Technical Writers 59,590
Telecommunications Equipment Installers and Repairers, Except Line Installers 50,940
Tire Builders 42,500
Tool and Die Makers 46,750
Training and Development Managers 87,630
Training and Development Specialists 57,180
Transportation Inspectors 65,650
Transportation, Storage, and Distribution Managers 86,090
Urban and Regional Planners 58,590
Veterinarians 79,820
Water and Wastewater Treatment Plant and System Operators 42,750
Web Developers 50,610
Wholesale and Retail Buyers, Except Farm Products 55,700
Writers and Authors 54,250
Zoologists and Wildlife Biologists 59,000

Sheet2

Sheet3

Statistics homework help

ANOVA

2

What is Analysis of Variance (ANOVA)?

• A Hypothesis Test to compare means

• How: Compares means or other estimates of variance for
each source of variation

• The underlying test used in many Designed Experiments

• Superior to regression because inputs do not have to be
continuous variables

3

Method

• Uses sums of squares, just like a standard
deviation, to evaluate the total variability of the
system

• Calculates “standard deviations” for each source
and subtracts the variability from the total

4

ANOVA Within vs Between

Within subgroup variation

Between subgroup variation

5

The F-Distribution

• Variance = Sum of Squared deviations/df

• There are two variances (Within and Between), the F statistic is the
ratio of the two variances. The ratio forms an F-distribution.

• The F-distribution depends on two sets of degrees of freedom – the
df from each variance: df1 for the Between and df2 for the Within

Error

Factor

MS

MS
F =

2

Within

2

Between
df,df

s

s
F

21
=

One Way ANOVA

Identical to a t-test if there are only two levels

One Way ANOVA Example

Donald P. Lynch, Ph.D. 8

Assumptions of ANOVA

1. Normality (not important)

2. Homogeneity of Variance (not important)

3. Sample is random (extremely important)

4. For multi-factor ANOVA input factors must be
independent (extremely important)

1. Verify with correlation
2. This will be demonstrated with regression

TW0-Way ANOVA

Multi-Factor ANOVA Example
Inputs Output

Statistics homework help

RUBRIC

Criterion 1

A – 4 – Mastery

Submission skillfully includes: an introduction, a matrix table, a conclusion, three recommendations

Criterion 2

A – 4 – Mastery

Submission skillfully includes a matrix table of the three data visualization tools whose pertinent features closely match the needs of the firm.

Criterion 3

A – 4 – Mastery

Thorough rating of ease of learning and use of the tool.

Criterion 4

A – 4 – Mastery

Thorough presentation of cost information including subscription and maintenance fees.

Criterion 5

A – 4 – Mastery

Thorough ranking of products including a single final recommendation

Statistics homework help

Research Articles

Research Articles – Main Parts

Abstract

Introduction

Methods

Results

Discussion

References

Research Article – Main Parts

Abstract

Provides a brief overview of the article

Introduction

Discusses previous research that led the authors to their current study and research question(s) and hypothesis(ses)

Methods

Describes the sample/participants, outlines the tests used in the study and what each was used to measure/assess

Results

Will include both written and visual demonstrations (e.g., tables, graphs, figures) of results of the statistical analyses that were conducted

Discussion

Provides a summary of results, what were the important findings/why the study was important, and conclusions/future directions

References

Lists all the references that were cited throughout the article

Where is the Purpose/ Hypotheses?

The purpose will sometimes be labeled as “Purpose” or “Objective” in the abstract

The purpose(s) and hypothesis(ses) can also be found at the END (typically the last paragraph) of the Introduction section

Lange, E., Kucharski, D., Svedlund, S., Svensson, K., Bertholds, G., Gjertsson, I., & Mannerkorpi, K. (2019). Effects of aerobic and resistance exercise in older adults with rheumatoid arthritis: a randomized controlled trial. Arthritis Care & Research, 71(1), 61-70.

4

How to tell is they are looking at differences/ relationships/or both

One, you can look at the wording of their hypotheses and what kinds of variables they are using

Two, it can also be helpful to look at which statistical analyses they used

Remember we learned in class that there are some statistical analyses that only look at differences and some that only look at relationships

And, for instance, if they used t-tests and regressions then we know they looked at BOTH differences and relationships

What types of variables did they use?

To identify their variables, you can look at their:

Hypotheses

Visual displays of the data (e.g., tables, graphs, figures)

It can be helpful to look at their tables/graphs if you are having trouble identifying which scale of measurement is used for their variables

If there are different groups in their tables/ x-axis of their graph – then we know it is a categorial variable

Tables and graphs will also show values – whether those values/numbers in the table/graph are all positive, or if they can be negative will help you determine which scale of measurement is being used as well.

Where do I find the tests they used?

Methods Section

The tests, or the tools/instruments, that were given to participants will be outlined in the Methods section

The tests are what the researchers gave participants/ what they had the participants DO in the study

In the example article to the left, what test was used?

One test used was the “Youth Sport Environment Questionnaire”

What did it measure?

It measured perceptions of task cohesion

Spink, K. S., McLaren, C. D., & Ulvick, J. D. (2018). Groupness, cohesion, and intention to return to sport: A study of intact youth teams. International Journal of Sports Science & Coaching, 13(4), 545-551.

7

Where do I find the Statistical Analyses

The statistical analyses section is typically:

At the end of the methods section

OR

Beginning of the results section

Sometimes the section is clearly labeled as “Statistical Analyses” or “Data Analyses”

Spink, K. S., McLaren, C. D., & Ulvick, J. D. (2018). Groupness, cohesion, and intention to return to sport: A study of intact youth teams. International Journal of Sports Science & Coaching, 13(4), 545-551.

8

Statistics homework help

Experimental Design

Introduction

• What is DOE?

• Why & when to use DOE?

• Main purpose of DOE: Gain knowledge with minimum expense

What is DOE?

• DOE is a structured method data collection & analysis for empirical curve fitting
• It begins with the statement of the experimental objective and ends with the reporting of the

results

• A systematic set of experiments which permits evaluation of the effect of one or more factors
without concern about extraneous variables or subjective judgments

• It is the vehicle of the scientific method giving unambiguous results which can be used for inferring
cause & effect

• Possible Objectives:
• Eliminate non-significant factor

• Estimate Y=f(x) relationship

• Design or process optimisation

• It may often lead to further experimentation (heuristic approach – with each step in
experimentation, new hypotheses are generated that need to be tested)

Why & When to Use DOE?

• If you know the physics, you don’t need experimentation

• DOE may be more expensive than other options. Consider other options before DOE

• Multi-Vari charts

• Stepwise Regression with historical data

• SPC & process control

• Geographic Analysis

DOE Purpose

• Gain knowledge to
• Improve something

• Optimise something

• Solve a problem

• DOE enables knowledge to be gained
• Efficiently

• Objectively

Terminology

•Response
• The independent variable

• Output

• Effect

• Y

•There may be more than one response variable!
• Be careful not to ignore response variables that are not the focus of the experiment

• An engineer wants to increase productivity, but not at the sacrifice of quality

• You want to reduce the electrical interference or a radio, but reception quality cannot be sacrificed

Terminology

•Factor
• The dependent variable

• Input

• Controlled variable

• X

•It is the variable under investigation.
• The variable settings are manipulated in a controlled way during the experiment

• May be quantitative or qualitative

Steps of DOE

1. Verify your measurement system

2. Build linear model (1st order)

• Pick many factors

• Screen out factors

• Eliminate confounding

3. Optimise non-linear model (2nd order or higher)

• Evolutionary Operation (EVOP)

• Response Surface Methodology (RSM)

Objective &
Planning
Phase

Screening
Phase

Confirmation
Phase

Optimisation
Phase

Define
experimental
objective and
purpose

Screen for
influential
variables (Xs)

Correlate analysis
results with the
actual process

Optimise the
response
variables (Ys)

DOE Process

Objective & Planning Phase Purpose

• Clearly define the purpose of the DOE (maximise, minimise, hit a target, or minimise

variance)

• Answer the question: “Is the purpose of the DOE consistent with the practical problem

statement?”

• Perform measurement system and stability assessments

• Objective phase often overlooked

Objective & Planning Phase Tasks

• What is the practical problem?

• What is the response variable?

• Is it the correct one? Is it the only one?

• Gauge repeatability & reproducibility; can we measure the expected changes in our response

variable(s)?

• What is our desired response?

• What is the objective (maximise, minimise, or hit target) in terms of response?

• Is the process stable?

Screening Phase Purpose

• Identify variables that have a significant effect on the response

• NOT interested in defining a mathematical relationship at this phase

• Goal is to determine the factors that are carried for further experimentation

Screening Phase Tasks

• What are potential X variables?

• What are the noise control and signal factors for the experiment?

• Select experimental design (set-up)

• What are the factor level settings?

• Perform (series of) screening experiment(s)

DOE Pre-Work

Noise Factors

Control Factors

Signal Factors Response
Product or
Process

1. Randomisation, Blocking
2. Measurement Systems Analysis;

Replication
3. Factor selection, factor level settings,

replication
4. Experimental Procedure

P-Diagram
1. Variation due to shift, batch,

environment, maintenance intervals,
machines, etc.

2. Measurement System Capability
3. Process Control
4. Discipline in performing experiment

Screening Model

Assume a linear relationship – identify
factors that move the response

Real predictive
relationship

Factor

Response

Screening Guidelines

• Only use two levels (assume linear model)

• Set the levels as far apart as possible, but realistic

• Include as many factors as possible

•Demonstration: <Factor Levels Simulation.xls>

Screening Designs

• Use standard designs that minimise the number of trials

• Plackett-Burman
• Orthogonal or balanced

• Taguchi copied these

• In Minitab or at the link below

• <Factorial Designs.xls>

Analysis of Variance

Demonstration: <SupportFiles\StandardDeviationSearch.xlsx>

Total variability

Between Groups (effects)

Total variability

Between Groups (effects)

Within Groups variability (noise)

Variance = (Sum of Squares) / df = Mean Square

Degrees of Freedom (DF)

• What is DF?

• With every increase in DF, the better you can predict what is going on

• With 3 factors and a screening design
• Y = c0 + c1X1 + c2X2 + c3X3 + error

• 9 = c0 + c1(-1) + c2(-1) + c3(+1) + error

• 7 = c0 + c1(-1) + c2(+1) + c3(-1) + error

• 5 = c0 + c1(+1) + c2(-1) + c3(-1) + error

• 19 = c0 + c1(+1) + c2(+1) + c3(+1) + error

•4 unknowns, 4 equations = perfect fit?

X1 X2 X3 Y

-1 -1 1 9

-1 1 -1 7

1 -1 -1 5

1 1 1 19

DF Example

Falsely
represents noise
in the system

Is the slope of the line > 0?

Factor A

0 10 20

R
e

sp
o

n
se

low highcentre point

DF Strategy

• Do Not replicate centre points

• Replicate subset of points – usually start with the treatments that generated

the highest & lowest response (if more replicates are required, go to the

treatment with the next highest and lowest response)

• Number of replications will always be a function of time and money

Repetitions vs. Replications
Repetitions Replications

Set-up Equip Set-up 1 Set-up 2 Set-up 3

Trial 1 Trial 1 Trial 2 Trial 3

Trial 2 Trial 4 Trial 5 Trial 6

Trial 3 Trial 7 Trial 8 Trial 9

Trial 4

Trial 5

Trial 6

Trial 7

Trial 8

Trial 9

Repetitions Replicates
Multiple observations of the same
experimental run (no adjustments
of the settings, average of
responses)

Duplication of a series of runs (takes
error setting up equipment into
account)

Minimises within subgroup error
Gives information to predict
experimental noise in the system

Adds Degrees of Freedom

Screening Design for 7 Factors with 8 runs

Exp. No. A B C D E F G Results

1 – – – + + + –

2 + – – – – + +

3 – + – – + – +

4 + + – + – – –

5 – – + + – – +

6 + – + – + – –

7 – + + – – + –

8 + + + + + + +

Randomise Trials

•Prevents a lurking (hidden) variable from influencing results

•Examples:

• Ambient temperature increasing from 15 °C to 30 °C

• Learning effects

• Experimenter fatigue

Why Do I Need Statistics?

• Paretos don’t always work

• Demonstration
• SupportFiles\Pareto.xlsx

• Show main effects plot

• Compute significance

Interactions

• Coupled effects – the response is dependent upon the input of two or more factors

• Confounded

• Aliased

• Are you healthy if you weigh 23 kg (50 lbs)?

• Yes, if you are 1.22 m (4 feet) tall

• Weight and height are called interacting factors

Interactions

•Y = c0 + c1A + c2B + c12AB

Column A = Column B × Column C

Demonstration: <Interaction.xls>

Trial

Factor

A B C

1 -1 -1 1

2 -1 1 -1

3 1 -1 -1

4 1 1 1

2-Way Interactions

A + BC

B + AC

C + AB

Resolution

• Resolution refers to the amount of information that may be obtained from a given
experiment.

• The higher the resolution, the more information may be obtained from the experiment (i.e.,
learn about interactions and higher order terms).

• For most experimentation, three resolutions are appropriate to discuss (III, IV, & V).

Resolution III: A design in which main effects may be separated from other
main effects, but not from interactions. That is, interactions are confounded
or aliased with main effects.

Resolution IV: A design in which main effects may be separated from other
main effects and two-way interactions (two factor), but two-way
interactions are confounded with other two-way and higher order
interactions.

Resolution V: A design in which main effects may be separated from other
main effects, and two-way interactions may be separated from other two-
way interactions, but higher order interactions are confounded.

Saturated Designs

•Beware of how software handles non-saturated designs

•Demonstration: <Dummy Variable.xls>

One Factor at a Time

0 6

1
2

1
8

2
4

3
0

3
6

0

16

32

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

X1

X2

9000-10000

8000-9000

7000-8000

6000-7000

5000-6000

4000-5000

3000-4000

2000-3000

1000-2000

0-1000

0 4 8

1
2

1
6

2
0

2
4

2
8

3
2

3
6

4
0

0

4

8

12

16

20

24

28

32

36

40

X1

X2

9000-10000

8000-9000

7000-8000

6000-7000

5000-6000

4000-5000

3000-4000

2000-3000

1000-2000

0-1000

C

A

B

X1

X2

D

Worse Case: Pure
Interaction

F = MA
V = IR

Approach:Change one factor at a time (from min to max)
while holding all other factors constant

Full Factorial

• Used to determine which factors have a statistically significant effect on the response

variable(s)

• Factors may be quantitative or qualitative

• At least one value of the response is observed at each treatment combination

• Normally the experiment is significantly larger due to the multiple treatment combinations

• No confounding is present in a Full Factorial

Fractional Factorial

• Used to determine which factors have a statistically significant effect on the response

variable(s)

• Factors may be quantitative or qualitative

• Goal is not to define a mathematical model, but to determine which factors should be

included in further experimentation

• Confounding is present in a Fractional Factorial

• Initial experimentation will utilise less runs than a Full Factorial

•Preferred Choice for Initial Screening Design

Example

• Screening

• Resolution separation

Response Surface
Methodology

2

Objective – Response surface methodology
• Develop conceptual understanding of response surface methodology (RSM)

• Describe method of steepest ascent

• Discuss response surface methodology modelling including characterising the
response surface

• Discuss designs for fitting response surfaces

• Describe analysis methods when multiple responses are present
0 6

1
2

1
8

2
4

3
0

3
6

0

14

28

-1500

-1000

-500

0

500

1000

1500

2000

2500

3000
2500-3000

2000-2500

1500-2000

1000-1500

500-1000

0-500

-500-0

-1000–500

-1500–1000

0 4 8

1
2

1
6

2
0

2
4

2
8

3
2

3
6

4
0

0

4

8

12

16

20

24

28

32

36

40

2500-3000

2000-2500

1500-2000

1000-1500

500-1000

0-500

-500-0

-1000–500

-1500–1000

Response surface methodology
• A “response surface” is a topographical representation of the

response over a region of the input variables

• Response Surface methods are simple curve fitting
• Use 2nd order polynomial

• Limitation: Real world is not 2nd order polynomials
• Sequential approach using conclusions from screening to reduce

experimental region

Maximum Minimum Saddle point Stationary ridge

Steps of response surface methodology

•Typically a sequential
experiment
• Start with response surface

over a large region

• Use results of larger
response surface to focus on
smaller region that may
contain optimum point

• Repeat as necessary

• May stop at any time and
use EVOP

Response surface models
Use second order polynomial approximations

• Include the linear effects

• Allow us to estimate curvature (squared terms)

• Model all second order interactions

Second order polynomial: Two factors
Y = a0 + a1A + a2B + a3A

2 + a4B
2 + a5AB

Second order polynomial: Three factors
Y = a0 + a1A + a2B + a3C + a4A

2 + a5B
2 + a6C

2 + a7AB + a8AC + a9BC

Type of response surface designs
• Box-Behnken design

• Minimal design points

• All factors are never set at their high levels simultaneously

• Central composite design

• Can incorporate information from a properly planned factorial

experiment

• Only need to add axial and centre points

Type of response surface designs
•Central composite design (CCD)
• Can incorporate information from a

properly planned factorial experiment

• Only need to add axial and centre points

•Box-Behnken design
• Minimal design points

• All factors are never set at their high
levels simultaneously

• Box-Behnken Design consists of
twelve “edge” points (shown as solid
dots) all lying on a single sphere about
the centre of the experimental region,
plus three replicates of the centre
point.

B

C

A

“Cube” + “Star”
+ Centre Points

“Face-centred”
CCD

Central composite designs

“Face centred””Circumscribed” “Inscribed”

-1

+1

Experimental set-up for 2 factors

Trial Factor A Factor B

1 -1 -1

2 -1 0

3 -1 1

4 0 -1

5 0 0

6 0 1

7 1 -1

8 1 0

9 1 1

Design using coded variables

Simplest design is 3×3 full factorial

Factor A

1

0

-1

0-1 1

*** Re-use trials from screening experiments ***

Response surface procedure

• The real world is not 2nd order polynomials

• Limit the size of the region modelled to improve accuracy

• Consider sequential RSM with each new RSM modelling a

smaller region

Sequential Simplex
Optimisation

3

EVOP – Sequential simplex optimisation
60

80

90

70

85

93

5

10

15

20

25

0

40 60 80 100 120

Fa
ct

o
r

B

Factor A

EVOP principles
• Evolutionary operation, abbreviated EVOP

• An evolutionary, iterative path of the steepest ascent method

for determining the optimum process setting

• Typically performed in manufacturing

• Small changes in factor settings with large sample sizes

• Non-disruptive to manufacturing process; experimental parts are

shippable

• Also valuable approach outside of manufacturing

• Small sample sizes

• Alternative to response surface methodology

EVOP principles
• Factor levels may be the boundaries for producing acceptable

(and saleable) products

• Can be run during normal production time

• Data from normal production runs provide input for

calculations of subsequent process parameter settings

• Process is repeated until optimum response variable is

obtained

Sequential simplex optimisation

Fixed step size

example

60

80

90

70

85

93

5

10

15

20

25

0

40 60 80 100 120

Fa
ct

o
r

B

Factor A

Sequential simplex fundamentals
• The number of trials in the initial simplex is k+1 (k is the

number of experimental factors)

• Factorial approach has at least 2k, and possibly 3k or 4k trials

• Only one new trial is required to move to a new area in the

space defined by the factors

• Factorial design requires at least 2k-1 trials

• Don’t have to worry about a mathematical model

• Decisions are based on ranking of vertices of our simplex

Sequential simplex fundamentals
• How does it work?
1. Choose initial simplex

2. Experiment at each setting
defined by vertices of simplex

3. Rank the vertices as best, next
best, and worst based on
response

4. Calculate “Reflection” of worst
point and experiment at the
reflection

5. Go back to step 3 and repeat
until optimum is reached

Variable X1

BEST (B) NEXT BEST (N)

WORST (W)

REFLECTION (R)

Choosing starting point
In manufacturing

• Start with small “region” to minimise disruption to process

Where you don’t need to worry about disrupting a

production process

• Start with a large “region”

• Large starting regions tend to converge on optimal solution

more quickly

“Sequential Simplex Optimization” – Walters, F.H., Parker, L.R., Morgan, S.L. and Deming, S.N.

www.chem.sc.edu/faculty/morgan/pubs/sequentialsimplexoptimization.pdf

Tips for simplex optimisation
• Make sure that you have a real difference in results –

confidence intervals

• Don’t be afraid to change sample sizes as vertices become

closer or farther apart

• If your simplex collapses, pick new vertices and start again

• For example, three points in a straight line

• Can happen if you run into a boundary for a variable

Sequential simplex fundamentals
• Fixed step size

• No other choice other than reflection

• Simplest form of simplex

• Issues with fixed size simplex model

• If large size step is used, the optimum point is never reached

• If small steps are used, it takes an excessive number of steps to

reach the optimum point

• Variable size simplex solves these issues

Sequential simplex fundamentals
• Variable size simplex

• Instead of a simple, fixed step sized reflections (R), there are

other options:

• double the length of the reflection (E)

• reduce the length of the expansion by 50% (Cr)

• produce the reflection in the opposite direction but at 50% of the

normal length (Cw)

• Makes the discrimination of the simplex variable

• Increases rate to arrive at optimum

Variable size simplex concept

B N

W

R

E

CR

CW

Variable X1

Rank

vertices

Try and

rank “R”

B

N

W

If R > B, Try E

– If E > B, use E

– Else, use R

If N <= R <= B,

use R

If W <= R < N,

use CR

If R < W,

use CW

Sequential simplex fundamentals
• Confidence intervals

• When entering new points in the Simplex, it is important to

determine that the new point is statistically different (with a

degree of confidence) from the other prior three points

considered

• This is accomplished by a form of hypothesis test of the means

• It is critical to perform this test when the Simplex begins to

converge on the optimum and the points grow progressively

closer together

Demonstration: <Simplex Confidence Intervals.xls>

Traps in sequential simplex

• Collapse of the simplex

– Can collapse if the aspect ratio of the shape becomes too large

– To avoid, monitor the vertices and re-start the simplex with new points if

collapse is evident

• Run into limit

– If the simplex falls outside the variable limit, the variable is set to the limit

– This could cause the simplex to collapse

– Consider re-starting with a small simplex in the best region

• Local vs. global optimum

– Multiple optimal points can cause the simplex to find a local optimum rather

than the global optimum

– To avoid, a large starting simplex or starting with a response surface is

advisable

Variable size simplex
• Tips for initial simplex:

• Allow sufficient room between the initial simplex and the

factor limits

• Select a range for the initial simplex such they are not within

one step of the factor limits

2014-11-06 Design of ExperimentsSlide 58

Comparison sequential simplex vs. RSM

Sequential simplex Response surface method

No underlying mathematical model Based on mathematical model

If “k” = # factors, you need (k+1) points to
start, with 1 additional point per step

If “k” = # factors, you will need 3k points
to start, and 3k points for each step

Seeks optimum “point”
Seeks optimum settings, with some
information on surrounding regions

Information on “path” to optimum
Information collected for “regions” of
operation

Better suited for ongoing manufacturing
process improvement

Better suited for design optimisation, or
brand new manufacturing process

Causes for a “noisy experiment”
• Measurement error

• Measured the wrong response

• Missed a significant factor

• Undisciplined experimental procedure

• Experimental procedure was not controlled

• Planning after research completed

• Should have blocked out noise

• No randomisation

• Levels were too close

• Interaction mistakenly used for degrees of freedom

When not to use experimental design
•If the relationship is defined with equations

representing the physical relationship – it is better just

to perform the calculations rather than try and derive

the relationship through experimentation

•Remember experimentation predicts the relationship

between the dependent and independent variables by

assuming a very simple mathematical model

20 3010
30

65

100

Statistics homework help

ANOVA

2

What is Analysis of Variance (ANOVA)?

• A Hypothesis Test to compare means

• How: Compares means or other estimates of variance for
each source of variation

• The underlying test used in many Designed Experiments

• Superior to regression because inputs do not have to be
continuous variables

3

Method

• Uses sums of squares, just like a standard
deviation, to evaluate the total variability of the
system

• Calculates “standard deviations” for each source
and subtracts the variability from the total

4

ANOVA Within vs Between

Within subgroup variation

Between subgroup variation

5

The F-Distribution

• Variance = Sum of Squared deviations/df

• There are two variances (Within and Between), the F statistic is the
ratio of the two variances. The ratio forms an F-distribution.

• The F-distribution depends on two sets of degrees of freedom – the
df from each variance: df1 for the Between and df2 for the Within

Error

Factor

MS

MS
F =

2

Within

2

Between
df,df

s

s
F

21
=

One Way ANOVA

Identical to a t-test if there are only two levels

One Way ANOVA Example

Donald P. Lynch, Ph.D. 8

Assumptions of ANOVA

1. Normality (not important)

2. Homogeneity of Variance (not important)

3. Sample is random (extremely important)

4. For multi-factor ANOVA input factors must be
independent (extremely important)

1. Verify with correlation
2. This will be demonstrated with regression

TW0-Way ANOVA

Multi-Factor ANOVA Example
Inputs Output

Statistics homework help

Student’s Name: Evaluator: Date:

LO 6. – Students will evaluate and apply selected analytics techniques to help enhance organizational competitiveness. (Assess in OPRE 605)

Guidelines

A key learning objective of this course is for you to be able to apply what you learn to solve novel problems that you encounter in your professional setting. As such, the final exam for this course is an individual project that integrates and applies the techniques covered in the course in a unique problem.

The project deadline is Friday, May 20, 2022.

You will have 5 minutes to briefly present your project in class on Thursday, May 12th.

TOPIC

Think about a domain you are very interested and/or experienced in and then think about aspects of it that are economic – issues of supply and demand, cost and profit, inventory management, appreciation/depreciation of value, entrepreneurial strategy, etc. What problems do you see in that domain that could benefit from an analytic model? Think outside the box and don’t hesitate to contact me if you need help or if you want feedback from me at any time.

Below is an outline of what material I expect to see in you final project report. 

GENERAL LOGISTICS:

As a reminder, these are INDIVIDUAL projects, and I will be expecting a unique submission from each student. 

Write your report in Word using double line spacing.

Save your data, model and analysis in an Excel file. Use label and sheet names to clearly organize your Excel file.

Paste any relevant table and chart in your report including labels and references in the text.

Use font Arial size 10 (or similar if not available in your system).

By midnight on the due date, upload your Word file and Excel data file in Sakai under Assignments. (10% of the points will be deducted for each day or fraction of day that work is submitted after the due date.)

You should plan to write a brief report (3-5 pages) that has the following sections:

Introduction – describe the problem you are trying to solve (e.g., What/when should I buy and sell shares in Stock X based on historical data? When should inventory be put on sale?), with some description of the topic domain (e.g., venture capitalism, clothing retail, restaurant management). Your problem should be rich enough to require a spreadsheet model and simulation or linear optimization.

Analytic Strategy – verbally describe your model/s of the problem, but also include an influence diagram and mathematical model, the assumptions your model/s make/s about the problem and the variables that are involved; also describe what data you will be using and how you will acquire it.

Findings and Implications – provide a visual model of the data and/or the model output/analytic results and a verbal explanation for what they mean to a decision maker faced with the problem you analyzed. If you had been hired by someone to consult on this problem, how you would advise them to act based on your findings.

References – provide verifiable citations for any published studies or documents that informed your project, as well as any external data set/s that you used to complete it.

Rubic:

Exceeds Standard

(accurate, relevant, multiplistic, logical, coherent)

Meets Standard

(correct, appropriate, dualistic, reasonable, consistent)

Below Standard

(inaccurate, inappropriate, singular, illogical, fragmented)

Score

Interpretation

Ability to interpret and frame a business scenario as an analytics problem

Presents information (data, ideas, or concepts) accurately and appropriately in familiar contexts

Reports information (data, ideas, or concepts) in familiar contexts with minor inaccuracies, irrelevancies, or omissions

Copies information (data, ideas, or concepts) often inaccurately, incompletely, or omits relevant information

25

Modelling

Ability to apply a business analytics technique to a new context

Applies formulas, procedures, principles, or themes accurately and appropriately in familiar contexts

Uses appropriate formulas, procedures, principles, or themes in familiar contexts with only minor inaccuracies

Labels formulas, procedures, principles, or themes inaccurately, inappropriately, or omits them

25

Analysis

Ability to interpret and evaluate (validate) solutions. Understanding of assumptions

Describes solutions, positions, or perspectives accurately. Identify some model limitations in general terms

Identifies simple solutions, over-simplified positions, or perspectives with only minor inaccuracies. Assumption nor limitation are considered

Names a single solution, position, or perspective, often inaccurately, or fails to present a solution, position, or perspective

25

Communication

Ability to explain the results within the context of the problem

Organizes a conclusion or solution that is complete, logical, and consistent with evidence presented

Connects ideas or develops solutions in a clear and coherent order

Offers an abbreviated conclusion or simple solution that is mostly consistent with the evidence presented, with minor inconsistencies or omissions

Arranges ideas or solutions into a simple pattern

Attempts a conclusion or solution that is inconsistent with evidence presented, that is illogical, or omits a conclusion or solution altogether

Lists ideas or expresses solutions in a fragmentary manner, without a clear or coherent order

25


Statistics homework help

Medicare Reimbursement

This assignment will test your knowledge of reimbursement methods of the Medicare program. Below, there are five scenarios that deal with the reimbursement of services provided to a patient enrolled in the Medicare program. Pay close attention to the details in each scenario such as whether the provider accepts Medicare or not. Use Chapter 9 (starting on page 308 of the textbook) to help you with calculating reimbursement. Show your work.

1. Mr. Allgood was just discharged from Meadowview Medical Center after receiving a procedure on his left leg. Mr. Allgood has Medicare coverage, which Meadowview accepts as a participating provider. Meadowview charges $215 for the procedure and the Medicare Physician Fee Schedule (MPFS) for the procedure is $150. What amount would Medicare be responsible for paying?

2. Mrs. Holloway has just received a bill from Oceanside Surgery Center regarding her recent outpatient surgery. Oceanside accepts Medicare assignment and charges $1,000 for her surgery. The MPFS for this surgery is $917. Mrs. Holloway was billed $200 from Oceanside Surgery Center. Considering that Mrs. Holloway is enrolled in the Medicare program, was she billed the correct amount? Explain why or why not.

3. Mr. Tee underwent a medical procedure on his lower back and is a Medicare patient. Mr. Tee has a good rapport with a local medical provider and wants them to do the procedure on him. This local provider is a non-participating provider and does not accept assignment from Medicare. The MPFS for the lower back procedure was $849. What amount is Medicare responsible for paying? How much is the patient responsible for paying?

4. Ms. Poppins has just received treatment for an ailing hip from New Scenery Medical Group which accepts Medicare. New Scenery Medical Group charges $73 for the treatment provided to Ms. Poppins, and the MPFS for the treatment is $70. If Ms. Poppins is responsible for $14, how much can New Scenery Medical Group write-off as uncollectible?

5.

Mr. Rogers was seen by Uptownship Health Care where he was provided medical services to address pain in his abdomen. This provider does not accept Medicare assignment and charges $750 for this type of service. The MPFS for the service is $615. Provide the amounts for the items listed below:

0. limiting charge,

1. Medicare’s portion,

2. the patient’s portion, and

3. the amount the provider can write off.

Resources

Statistics homework help

Discrete Distributions

Discrete Distributions

• Poisson

• Geometric

• Hypergeometric

• Binomial

What is Discrete Data?

• Data which describes distinct attributes or outcomes
• Pass/Fail

• Red/Green

• Large/Small

• Go/No-Go

Poisson Distribution

• Poisson is used to model rates
• Defects per unit

• Occurrences per hour

• Represents the probability of “x” occurrences in a fixed interval
• Assumptions: the probability of occurrence in an interval must be

proportional to the length of the interval, and the number of occurrences per
interval is independent.

• There is no upper bound to the number of occurrences
• In modeling defects per unit, there is theoretically no upper limit

• In modeling defective units per shipment, the upper bound is the number of units
shipped, therefore Poisson could not apply

Poisson Distribution

• Exact value of x: p(x,m) = (e-m mx)/x!

• Prob(x,m) = Probability of Occurrence

• x = number of occurrences

• m = rate of occurrence
(defects per unit, occurrences per hour, etc.)

• Cumulative value of x:
Sp(i,m)= S(e -m mi) /i!
i=0

x

i=0

x

x!

e
)p(x,

x
μ

μ
μ−

=

Poisson Distribution – Example

• Given an average of 5.5 warranty claims per month
• What is the probability of exactly 3 claims in a month?

• What is the probability of less than 3 claims in a month?

• What is the probability of more than 3 claims in a month?

Geometric Distribution

• Geometric Distribution is used to model the the probability of first
occurrence (success or failure)
• The number of trials is the variable

• The number of occurrences is fixed (at 1)

• The probability of occurrence from trial to trial is constant

• There is no upper bound to the number of trials required

Prob(x,p)= p(1-p)(x-1)

X = number of trials to first occurrence

p = probability of occurrence (per trial)

Example

• An event has historically averaged a success rate of 0.247 on a single
trial, what is the probability that more than or equal to 5 trials are
required to obtain the first success?

Hypergeometric Distribution

• Used to model the number of successes given a fixed number of trials
and two possible outcomes on each trial
• The probability of success on one trial is dependent on the outcome of the previous trial

• Example: Dealing cards from a deck — the odds of getting an Ace on the first card is 4/52. If the
first card is not not replaced, the odds of getting an Ace on the second card depends on whether
the first card was an ace (it’s either 4/51 or 3 out of 51).

• Sampling without replacement

=

p(x,N,n,m) =

m

x

N-m

n-x

N

n

This nomenclature
denotes a “Combination”

(number of possible
combinations)

a

b

a!
b!(a-b)!

m = number of occurrences in
population

x = number of occurrences in sample

N = population size

n = sample size

Cumulative Probability = Sp(i,N,n,m)
i=0

x

Hypergeometric Distribution

Exercise
• A sample of 8 items is taken from a population of

20 containing 12 blue items.

• What is the probability of obtaining less than 5
blue items?

Binomial Distribution

• Used to model the number of successes given a fixed number of trials
and two possible outcomes on each trial
• The probability of success is independent from trial to trial

• Example: dealing cards from a deck, but putting the card back in and reshuffling after each card is
drawn.

N!

x!(N-x)!
px(1-p)(N-x)p(x,N) = N = Number of trials

x = Number of occurrences

p = Probability of
occurrence

Example

• A plant produces marbles, and 18.5% of all marbles produced are red.

• What is the probability of selecting more than 3 red marbles in a
randomly selected sample of 5 marbles?

Modeling a Rate, with

no Upper Bound for

number of

Occurrences?

Poisson

Looking for the

Probability of First

Occurrence?

The Random variable is

number of trials

Looking for Probability of

Occurrence,

Samples pulled from fixed

population with no

replacement?

Looking for Probability of

Occurrence, Probability

Constant from Trial-to-

Trial?

Geometric

Hyper-

Geometric

Binomial

Yes

Yes

Yes

Yes

No

No

No

Start

Roadmap

Exercises

2008-10-01 © SKF Group Slide 16
SKF (Group Six Sigma) 1.07 Basic
Statistics

Exercises

Exercises

Exercise

Real Example With Data Changed

• 100,000 Hub Units Shipped

• A hub unit is found with no retainer nut after accident

• Five thousand units are inspected and another hub unit is found with no locking nut

• What is the expected number of hub units with no locking nut?

• What is the upper 90% confidence limit for this number?

• Should there be a recall? Think beyond statistics.

Statistics homework help

Systems Engineering & Voice
of the Customer

US Automotive Recalls
Vehicle Sold

(Millions) Vehicles Recalled

2011 2012 2013 2011 2012 2013

Toyota 1.6 1.7 2.2 219% 312% 241%

Honda 1.2 1.4 1.5 325% 243% 187%

BMW 0.2 0.3 0.3 150% 200% 300%

Hyundai 1.1 1.3 1.3 109% 138% 169%

Chrysler 1.4 1.4 1.8 57% 76% 261%

Ford 2.1 2.2 2.5 157% 64% 48%

Nissan 1.0 1.0 0.9 30% 100% 133%

GM 2.5 2.6 2.8 68% 58% 54%

Slide 2

System understanding

HoQ1→Boundary→HoQ2→P-diagram→DFMEA→PFMEA→SCIF→Control plan

HoQ1→Boundary→HoQ2→P-diagram→DFMEA→PFMEA→SCIF→Control plan

HoQ1→Boundary→HoQ2→P-diagram→DFMEA→PFMEA→SCIF→Control plan

HoQ1→Boundary→HoQ2→P-diagram→DFMEA→PFMEA→SCIF→Control plan

System validation plan

System verification plan

Sub-system verification plan

Component verification plan

Time line

System

Sub-
system

Component

System

Sub-
system

Requirements Flow Down Example

We Must Know the
Mathematical Relationship to
Flow Down Requirements
• What are the options if the engineering is not

known?
• Safety factor

• Pass responsibility to customer

• Refuse the business

• Increase price to compensate for the additional risk

• Use experiments to create empirical models

• Basic research

Never accept a known risk for safety or compliance with
government regulations

Slide 6

Relationships

Boundary
diagram

Parameter
diagram

Design
FMEA

R&R
matrix

HoQ #1

Process
FMEA

Critical
characteristics
identification
form

Manufacturing
control plan

Field
performance

Project goals Knowledge storage & re-use is

critical

Our Influence Over Risk

Start

up

RISK MANAGEMENT PROCESS

(APQP)

ABILITY TO
INFLUENCE RISK

Design &

Develop

Product

Design &

Develop

Process

Product &

Process

Validation

RISK

Start

up

RISK MANAGEMENT PROCESS

(APQP)

ABILITY TO
INFLUENCE RISK

Design &

Develop

Product

Design &

Develop

Process

Product &

Process

Validation

RISK

Time
Start

up

RISK MANAGEMENT PROCESS

(APQP)

ABILITY TO
INFLUENCE RISK

Design &

Develop

Product

Design &

Develop

Process

Product &

Process

Validation

RISK

Start

up

RISK MANAGEMENT PROCESS

(APQP)

ABILITY TO
INFLUENCE RISK

Design &

Develop

Product

Design &

Develop

Process

Product &

Process

Validation

RISK

Time

DEFINE IT RIGHT

House of Quality (HoQ)
• Features:

• Inputs from customer

• Measurable functional requirements to
test against

• Targets and limits set by customer

• We will use rooms 1 and 3 to assist in
creating the FMEA

• May be:
• Used as an aid when completing a CSCM or

• Not used if the CSCM is sufficient in define
customer needs

7

3

5

4

6

2

8

Direction of improvement

Calculated
importance

Competitive
comparison of

customer
ratings

Conflicts

Correlations

Competitive
benchmarks

Targets
and limits

Functional requirements

1

C
u

st
o

m
e

r
e

x
p

e
ct

a
ti

o
n

s

Fast Car Example

91 3 9

Types of Requirements
• Functional Requirements

• Define what functions need to be done to accomplish the mission objectives
• Example

• The Thrust Vector Controller (TVC) shall provide vehicle control about the pitch and yaw axes.

• This statement describes a high level function that the TVC must perform.

• Statement has form of Actor – Action Verb – object acted on

• Performance Requirements (Specification)
• Define how well the system needs to perform the functions
• Example: The TVC shall gimbal the engine a maximum of 9 degrees, +/- 0.1 degree

• Constraints
• Requirements that cannot be traded off with respect to cost, schedule or performance
• Example: The TVC shall weigh less than 120 lbs.

• Interface Requirements
• Example: The TVC shall interface with the J-2X per conditions specified in the CxP 72262

Ares I US J-2X Interface Control Document, Section 3.4.3.

• Environmental requirements
• Example: The TVC shall use the vibroacoustic and shock [loads] defined in CxP 72169, Ares 1

Systems Vibroacoustic and Shock Environments Data Book in all design, analysis and testing
activities.

• Other -illities requirement types including availability, reliability, maintainability, etc.

Attributes of Acceptable Requirements
• A complete sentence with a single “shall” per numbered

statement

• Characteristics for Each Requirement Statement:
• Clear and consistent – readily understandable

• Correct – does not contain error of fact

• Feasible – can be satisfied within natural physical constraints,
state of the art technologies, and other project constraints

• Flexibility – Not stated as to how it is to be satisfied

• Without ambiguity – only one interpretation

• Singular – One actor-verb-object requirement

• Verify – can be proved at the level of the architecture applicable

• Characteristics for pairs and sets of Requirement Statements:
• Absence of redundancy – each requirement specified only once

• Consistency – terms used consistent

• Completeness – usable to form a set of “design-to” requirements

• Absence of conflicts – not in conflict with other requirements or
itself

• Clarified with boundary and P-diagrams

• NASA Systems Engineering Handbook for Reference

Requirements Definitions Mistakes
• Writing implementations (How) instead of

requirements (What)
• Forces the design

• Implies the requirement is covered

• Using incorrect terms
• Use “shall” for requirements

• Avoid
• “support”

• “but not limited to”

• “etc”

• “and/or”

• Using incorrect sentence structure or bad grammar

• Writing unverifiable requirements
• E.g., minimize, maximize, rapid, user-friendly, easy,

sufficient, adequate, quick

• Requirements only written for “first use”

Did any Changes or Improvements Have a Negative
Impact on Another Function?

Potato Cannon Exercise
• Customer wants to win the potato cannon contest

• Fire a potatoes into squares
• Square are 20 meters long on each side

• Center of square is 150 meters away

150 meters

10 meters

Potato Cannon
• How it works

• Potato is pushed into the sharpened barrel which cuts
potato to size

• Hair spray (propane – C3H8) is added at the back end

• Spark creates explosion

• Demonstration

• Components
• Loading rod

• Combustion Chamber, end cap, end cap connector and
igniter

• Barrel & reducer

• Teams of 3 or 4

• Use “TBD” if exact values
cannot be determined

• Additional Links
• Search for potato cannon fails

• Fire

Barrel

Combustion

Chamber

Igniter

Reducer

End Cap Connector
End Cap

Igniter

Seal

Scoping and Definition of Responsibility
• The customer needs a solution and is looking to SKF to deliver some functions

• To deliver the functions, we need clear definition of the functions, and detail
regarding the conditions our product is expected to work under
• The CSCM provides the function definitions

• The boundary diagram contains these functions and
• the operating conditions

• responsibility for each component

Our Solution

System Part 1 System Part 2

System Part 3

Condition 1

Condition 2

Condition n

Function 1

Function 2

Function p

Las Vegas High Roller

Las Vegas High Roller
• Multiple companies designing simultaneously

• Used the boundary diagram to:
• Understand the tolerances of all interfaces

and non-interfacing parts that potentially
impact the bearing

• Define loading
• Wind loads
• Seismic events

• Define bearing handling and installation

• This was challenging
• Strengthened hub design
• Changed spindle design
• Given responsibility for installation procedure

and equipment design
• Automatic lubrication
• Automatic Condition monitoring

Las Vegas High Roller Boundary Diagram

Spindle

Tapered

sleeve

Housing

Grease

Support

Legs

Brace

Leg

CablesRim

Mounting

ring
Cabin

Drive

system

Spherical

roller

bearing

Inputs

•Loads (Cable, wind, passengers)

•Contamination (dust, water)
Desired Outputs

•Fatigue life

•Wheel rotation

•Accommodate heat growth

Undesired Outputs

•Friction

•Vibration

Operating conditions analyzed:

– Service case 1

– Service case 2

– Service case 3

– Service case 4

DESIGN IT RIGHT

What Could Go Wrong?
• Now the boundary of our solution is clearly defined, we should

question what could cause the functions not to be delivered.

• Our solution will work and be used in some uncontrolled

conditions. These external factors are called noise factors.

• The standards define 5 types of noise factors:

• Piece to piece variation (tolerance stack-ups)

• Degradation over time

• Environment

• Customer use and abuse

• System interaction

• Listing these potential noise factors is key, as these noise factor will

become the potential causes of failure.

Unintended Functions
• Unintended Failures

• Electric car burns down garage (Alleged)

• “Toyota announced it was recalling 7.4 million vehicles to repair power-window switches
that can break down and pose a fire risk”

• Sooner or later everything will fail
• 100 year old car

• Modified car (Pimp my Ride)

• How is a car’s brake system designed to fail safe?

• The DFMEA should be used to
• Anticipate failures and ensure failures are as benign as possible

• Limp home mode in a vehicle

• Assure no injuries

• Boeing considered encapsulating dreamliner batteries in fire proof container

• Explore and eliminate unintended failure modes

• Other unintended failures
• Scully

• McDonnel Douglas

Foreseeable Use & Abuse

Potential Causes
• Potential causes of failure are taken from the P-

diagram

• The engineer is NEVER the failure cause; examples
• Wrong bolt plating specified

• Lower plating thickness is incorrect

• In identifying potential causes of failure, use concise
descriptions of the specific causes of failures
• Bolt plating allows rusting from exposure to humidity

• Potential cause of failure is defined as an indication
of how the design or process could allow the failure
to occur, described in terms of
• Something that can be corrected or can be controlled

• Something remedial action can be aimed at

• Something that can be identified as a root cause

• The system allowed or even facilitated the failure
cause – the system must be changed

Failure Modes
• How can the function not be

delivered?

• There are 4 potential failure modes:
• No function at all

• Intermittent function

• Degradation of performance

• Unintended function

Identification of Potentially Special Characteristics
• Utilize two stages of special characteristics

• Potential
• Confirmed

• Potential special characteristics are identified by
• Design – as a rule-of-thumb 80% of all variation

• Cannon animation
• Reservoir example

• ISO or other standard
• Customer
• Supplier

• Potential special characteristics are identified on the drawing and SCIF
• Manufacturing (or the supplier) confirms if special controls are needed

for these characteristics based on capability (including special causes)
• There is no set capability limit
• Maintain flexibility based on severity and industry

• The SCIF records the confirmation decision and reasoning
• The decision is reviewed as part of the ECM process

Solution Space for Projectile Distance
• Solution 1

• Angle 70°± 1°

• Velocity 316.5 ± 1 ft/sec

• Solution 2

• Angle 70°± 0.8°

• Velocity 316.5 ± 2.5
ft/sec

• Solution 3

• Angle 45°± 1°

• Velocity 253.8± 6.2
ft/sec

• Solution 4

• Angle 45°± 2°

• Velocity 253.8± 6.0
ft/sec

• Solution 5

• Angle 45°± 5°

• Velocity 253.8± 4.5
ft/sec

2100 ft

1900 ft

2000 ft

Gearbox Example

Only one special

characteristic

Airbus Super Puma Crash
• What items should be added to the

P-diagram?
• Customer use & abuse (Dropped

gearbox)
• This has been moved to the boundary

diagram

• Piece-to-piece (worst case roller &
raceway profiles)

• What is the failure cause?
• Worst case roller & raceway profiles &

max shock load

• The accident could have been
prevented if there was a warning
• Detection of a metal particle
• Vibration

Video

Failure Effect
• The effects should always be stated in terms of the

specific project, system, product or process analyzed​

• Remember that a hierarchical relationship exists
between the component, sub-system, and system levels.
For example, a part could fracture, which may cause the
assembly to vibrate, resulting in an intermittent system
operation.

• Do not list effect beyond your area of responsibility​

• Brake tube designer cannot have “No Brakes” as effect​

• The effect is “Loss of Brake Pressure”​

• State clearly if the failure mode could impact safety,
non-compliance to regulations

Severity
• Severity is defined as how serious the effects of a failure

would be should they occur

• It is important to realize that each failure mode may have
more than one effect, and each effect can have a different
level of severity

• It is the effect which is being rated and not the failure,
therefore each effect should be assigned its own severity
ranking

• A scaling system from 1 to 10 should be used, with 10 being
reserved for the most severe failure modes

• You may have to defer to the customer
• Build to print PFMEA with no access to DFMEA

Is the Product Designed Right?

• Green specifications – provide the customer’s
functions

• Blue specifications – artificially tight providing a
safety factor
• Improperly built parts may deliver the customer’s functions

• Red specifications – the design is not correct
• Properly produced parts will not always deliver the

customer’s functions

What Happens if You Drive Off with the Gas
Pump Nozzle Still in the Car?

• This should be on the P-diagram
• Customer use (and mis-use)

• What was the severity of this incident in 1950?

• What is the severity of this incident today?
• The hose that attaches the nozzle to the gas pump is designed to break into two

pieces when a certain amount of force is applied to it

• Next time you’re at the gas station, check the hose for a metal coupling

• That’s the break-away point

• Once the hose is broken and you’re off on your merry way, check valves in the
hose keep fuel from leaking out and creating a hazard

• Severity can only be improved by a design change
• Failure mode designed out

• This is the design control

• It is important to keep this information in the DFMEA so future designs don’t
repeat the mistake
• Remove the coupling for cost save

• Remove check valves for cost save

What Happens if You Drive Off with the Gas
Pump Nozzle Still in the Car?

Controls
• There are two types of design controls to consider

• Prevention controls
• Aim to eliminate or prevent the cause of the failure mechanism or the failure mode from

occurring

• Aim to reduce rate of occurrence

• The preferred approach is to use prevention controls
• Gives a more robust product or process

• Initial occurrence rankings will be affected by the prevention controls

• Prevention controls
• Predict performance based on scientific knowledge or

• Ensures performance based on historical experience

• Design out failure mode

• Examples of prevention controls
• Fail-safe designs (if two wheel speed sensors disagree, the ABS system is disabled)

• Follow proven design and material standards (internal and external)

• Calculation & Simulation studies (computing the maximum deflection by computing deflection for
every possible combination of tolerances)

• Use of components proven under less stressful conditions

• Error-proofing (using non-symmetrical parts to make it impossible to install a component backwards)

Controls
• Detection controls

• Aims to identify the existence of a cause that results in a mechanism of
failure

• The detection ranking is associated with the best detection control listed
in the current design control detection column

• Should include identification of those activities which detect the failure
mode as well as those that detect the cause, and could include:
• Prototype testing

• Validation testing

• Design of experiments including reliability testing

• Mock-up using similar parts

• A suggested approach to current design control detection is to assume
the failure has occurred and then assess the capabilities of the current
design controls to detect this failure mode

• Warning
• Often the detection method is assumed to be good because no parts with

the failure mode have passed through the detection method

How Much Confidence Do You Have?
• Compare this to a design change, or

a choice between two materials
• Is George Bush equivalent to the

university player?

• They are both one-for-one (the same
performance)

• What should be considered for a DV
test
• Choose parts and loads that target the

highest risk areas
• Minimum thickness

• Highest wavieness

• Maximum preload

• Highest load, etc

Occurrence Rating

• The occurrence ranking is solely a function of prevention
controls

• No prevention control gives a ranking of 10

• Ranking of 1
• DFMEA: perfect knowledge of engineering with calculations at worst

case

• PFMEA: perfect error proofing or PPM less than 1

• This forces a separation of the prevention and detection
controls and strengthens the thinking of prevention over
detection

• Ideally, prevention=1 and detection=10

• Weaker prevention mandates stronger detection

Detection Rating
• The detection rating is determined by how well a test

can discover the failure mode or effect

• The rating is dependent on:
• The correlation of the test to real world conditions

• The parts tested
• If parts built very close to nominal are tested, the detection test

provides little value

• The best test utilizes parts built close to the worst case condition that
aggravates the failure mode or effected targeted

Priorities
• Severity is the primary driver

• Action Priority (AP)
• Low, Medium or high based on a combination of severity, occurrence

and detection

• Risk Priority Number (RPN)
• This is calculated by multiplying the 3 rankings recorded for severity,

occurrence and detection
RPN = Severity (S) * Occurrence (O) * Detection (D)

• RPN can range between 1 and 1000

• The use of an RPN threshold is NOT a recommended practice for
determining the need for actions
• Establishing such thresholds may promote wrong behavior (trying to justify

a lower occurrence or detection ranking value to reduce the RPN)

• This type of behavior avoids addressing the real problem that underlies the
cause of the failure mode and merely keeps the RPN below the threshold

• IF customers require actions based on thresholds, we shall follow the
customer requirements

AP

Recommended Actions

• The intent of recommended actions is to improve
the design

• Identifying these actions should consider reducing
rankings in the following order:
• Severity

• Occurrence

• Detection

• Be sure to include any actions that may be the
responsibility of the customer

• Never list a recommended action without a
completion date and responsibility for actions
related to safety or adherence to government
regulation

Robust Design Example
Cost was

reduced by

32% while

the process

capability

was

increased by

132%

BUILD IT RIGHT

The Transition from the DFMEA to the PFMEA
• The drawing has so many characteristics … how do I control them all?

• When creating the DFMEA, the characteristics with the biggest impact and
severity on the functions to be delivered were identified as potentially
special characteristics

• Other characteristics must also be controlled, but the consequences of the
non-special characteristics does not warrant the level of oversight that
must be taken with special characteristics

• Special characteristics are only potential at the design phase;
manufacturing may have error proofing or outstanding capability, that
eliminates any need for special controls

The Transition from the DFMEA to the PFMEA

• The Special Characteristics Information Form (SCIF) lists all the potentially
special characteristics from the DFMEA, eliminating the possibility of
overlooking a potentially special characteristic

• The SCIF also records the origin of the characteristic
• Was the characteristic determined from an engineering calculation?

• Was the characteristic flowed down by our customer?

• Was the characteristic flowed up by a supplier?

• Is the characteristic required by a standard?

• The SCIF also records why each characteristic was confirmed or not, and
what controls are in place for those characteristics confirmed

Transition to the PFMEA with the SCIF
• Forms the bridge from the DFMEA to the PFMEA

• Prevents Special Characteristics from being misses

Internal

PFMEA
• What do we have now :

• The specifications for all characteristics

• Potentially special

• Not potentially special

• Now we have to determine how to build the product to specification

• We have the requirements for the final part

• What are the requirements for the intermediate steps?

• What are the requirements for purchased material?

• How do we ensure purchased material conforms to our specifications?

Product Flow

• Just like functions are flowed down from the end
customer to sub-systems and eventually components,
the manufacturing characteristics needed to deliver
these functions are flowed back from the final assembly
to previous manufacturing steps and eventually
purchased materials

• The inputs for each step are the required outputs for
the previous step

What Could Go Wrong?
• Now the boundary for each manufacturing step is clearly defined, we should question what could

cause the characteristics not to be achieved.

• There are only 4 potential failure modes:
• No characteristic (part not hardened)
• Characteristic not achieved for the entire part (roughness is OK for 90% of the raceway, but

not the remaining 10%)
• Degradation of performance (part is hardened, but not to specification)
• Unintended function (part is scratched)

• There is variability in manufacturing. This variability is defined by noise factors.

• The standards define 5 types of noise factors:
• Man
• Machine
• Material
• Measurement
• Environment

• Listing these potential noise factors is key, as these noise factor will become the potential causes of
failure.

People are not the Problem
• The system is always at fault

• Do not blame the operator

• Do not blame the engineer

• Root cause is found by determining how the system allowed a
defect to be created and escape

• Example
• The label is placed in an incorrect position on a box

• 8D corrective action – the operator was sent to training

• Noooooooooooooo!

• Why did the system allow the operator to incorrectly place the label?
• No orientating fixture?

• Poor light?

• What can be done to prevent an operator from locating the label incorrectly?

What Happens if the Characteristics are not Delivered

• If a special characteristic is produced outside the green
specification, it does not matter if design determined the
specification wrong, or if the part was produced wrong, the
result is the same

• This must be reflected in the PFMEA; the severity and the
effect in the PFMEA must be the same as in the DFMEA

• The PFMEA also includes an internal severity ranking
• Is there a possibility of injury?

• What is the severity of finding a defect at the final production step
as opposed to immediately detecting the defect?

DFMEA & PFMEA

• If the failure mode, severity or effect is updated in the DFMEA, the PFMEA must
also be updated

Can we Build the Part to Specification

• How strong is our manufacturing knowledge?
• Can I predict the process outputs from inputs

(machine settings)?

• Is my SOP reliable given the input conditions
specified on the boundary diagram?

• Are error proofing methods in use, and how
effective are they?

• This ability to predict function performance
provides a probability of the failure to produce
the part to specification, and is assessed with
the Occurrence rating

Why Occurrence Does Not Come From Defect Data

• Green specifications – provide the customer’s
functions

• Blue specifications – artificially tight providing
a safety factor
• Improperly built parts may deliver the customer’s

functions

• Red specifications – the design is not correct
• Properly produced parts will not always deliver the

customer’s functions

• Case 1
• Red specifications, but Cpk

is very good, and all
production is within the
blue lines

• DFMEA occurrence should
be high, and PFMEA
Occurrence should be low

• Case 2
• Blue specifications, and

Cpk is poor resulting
production between
Green and Blue

• DFMEA occurrence should
be low, and PFMEA
Occurrence should be high

Can We Build the Part to Specification?

• How strong is our assessment program?
• Are all characteristics measured?

• Are characteristics measures at a rate of 100% of
sampled?

• How much measurement error is present?

• Has gage R&r been removed from the specifications?

• How often are known good and known bad parts
measured?

• Are statistical process control or trend charts used?

• This ability to measure characteristics provides a
probability of our ability to detect the failure of our
manufacturing process to deliver the required
characteristics, and is assessed with the Detection
rating

Purchased Material

• Receiving is a process

• What are the requirements?

• What are the controls?
• Prevention

• Supplier certification

• Supplier audits

• Require supplier to send data with each shipment

• Electronic access to supplier data

• Detection
• Incoming inspection

Manufacturing Control Plan
• The controls in the PFMEA become the Manufacturing Control Plan
• Additional information in the control plan

• Measurement assurance activities
• Reaction plans

• Following the Manufacturing Control Plan does not ensure zero defects
• The occurrence and detection rankings determine the effectiveness of

the manufacturing controls
• The effectiveness of the manufacturing controls combined with the

severity ranking highlights internal and external quality risks
• Highlighting these risks is a key part of business and technical gate

reviews
• The recommended actions portion of the PFMEA provides options for

mitigating these risks

Statistics homework help

RUBRIC for ORIGINAL RESEARCH PROJECT

Criteria

Expert

Proficient

Apprentice

Novice

Introduction

[Introductory

paragraph(s),

literature

review,

hypotheses or

propositions]

 Clearly identifies and

discusses research

focus/purpose of

research

 Research focus is clearly

grounded in previous

research/theoretically

relevant literature

 Significance of the

research is clearly

identified (how it adds

to previous research)

 Hypotheses/propositions

are clearly articulated

 Limited discussion of

research focus/purpose

of research

 Research focus is less

well-grounded in

previous

research/theoretically

relevant literature

 Significance of the

research is not as

clearly identified (how it

adds to previous

research)

 Hypotheses/propositions

are described but not as

well articulated

 Minimal discussion of

research focus/purpose

of research

 Research focus is not

well-grounded in

previous

research/theoretically

relevant literature

 Significance of the

research is not clearly

identified (how it adds

to previous research)

 Hypotheses/propositions

are not well articulated

 Little or no discussion of

research focus/purpose

of research

 Research focus not

grounded in previous

research/theoretically

relevant literature

 Significance of the

research is not

identified (how it adds

to previous research)

 Hypotheses/propositions

are poorly articulated or

are absent altogether

Research

Methods

 Provides accurate,

thorough description of

how the data was

collected, what/how

many data sources were

analyzed, plan of

analysis or

measurement

instrument, research

context

 Reflection on social

situatedness/reflexivity

and how it may

influence data collection

and interpretation is

thorough and insightful

 Description of how the

data was collected,

what/how many data

sources were analyzed,

plan of analysis or

measurement

instrument, research

context is adequate but

limited.

 Reflection on social

situatedness/reflexivity

and how it may

influence data collection

and interpretation is

adequate but limited

 Description of how the

data was collected,

what/how many data

sources were analyzed,

plan of analysis or

measurement

instrument, research

context is somewhat

confusing/not clearly

articulated.

 Reflection on social

situatedness/reflexivity

and how it may

influence data collection

and interpretation is

limited and lacks insight

 Description of how the

data was collected,

what/how many data

sources were analyzed,

plan of analysis or

measurement

instrument, research

context is very

confusing/not

articulated sufficiently.

 Reflection on social

situatedness/reflexivity

and how it may

influence data collection

and interpretation is

severely limited, lacks

insight, or is absent

altogether

Results

 Results are clearly

explained in a

comprehensive level of

detail and are well-

organized

 Tables/figures clearly

and concisely convey

the data.

 Statistical analyses (if

used) are appropriate

tests and are accurately

interpreted.

 Results are explained

but not as clearly, level

of detail is not as

sufficient, and there

are some

organizational issues

 Tables/figures are not

as clear/concise in

conveying the data.

 Statistical analyses (if

used) are appropriate

tests but are not

accurately interpreted.

 Results are not very

clearly explained, level

of detail is insufficient,

and there are more

organizational issues

 Tables/figures are not

clear/concise in

conveying the data.

 Statistical analyses (if

used) are inappropriate

tests and/or are not

accurately interpreted.

 Results are not clearly

explained, level of detail

is severely insufficient,

and there are serious

organizational issues

 Tables/figures are not

clear/concise in

conveying the data.

 Statistical analyses (if

used) are inappropriate

tests and/or are not

accurately interpreted.

Conclusions

 Interpretations/analysis

of results are thoughtful

and insightful, are

clearly informed by the

study’s results, and

thoroughly address how

they supported, refuted,

and/or informed the

hypotheses/propositions

 Insightful discussion of

how the study relates to

and/or enhances the

present scholarship in

this area

 Suggestions for further

research in this area are

insightful and thoughtful

 Interpretations/analysis

of results are sufficient

but somewhat lacking

in thoughtfulness and

insight, are not as

clearly informed by the

study’s results, and do

not as thoroughly

address how they

supported, refuted,

and/or informed the

hypotheses/proposition

 Discussion of how the

study relates to and/or

enhances the present

scholarship in this area

is adequate.

 Suggestions for further

research in this area

are adequate.

 Interpretations/analysis

of results lacking in

thoughtfulness and

insight, are not clearly

informed by the study’s

results, and do not

adequately address how

they supported, refuted,

and/or informed the

hypotheses/propositions

 Discussion of how the

study relates to and/or

enhances the present

scholarship in this area

is limited.

 Suggestions for further

research in this area are

very limited.

 Interpretations/analysis

of results severely

lacking in thoughtful

ness and insight, are

not informed by the

study’s results, and do

not address how they

supported, refuted,

and/or informed the

hypotheses/propositions

 Discussion of how the

study relates to and/or

enhances the present

scholarship in this area

is severely limited

and/or absent

altogether.

 Suggestions for further

research in this area are

severely limited and/or

absent altogether.

Documentation

of Sources,

Quality of

Sources

 Cites all data obtained

from other sources. APA

citation style is

accurately used in both

text and bibliography.

 Sources are all scholarly

and clearly relate to the

research focus.

 Cites most data

obtained from other

sources. APA citation

style is used in both text

and bibliography.

 Sources are primarily

scholarly and relate to

the research focus.

 Cites some data

obtained from other

sources. Citation style is

either inconsistent or

incorrect.

 Sources are not

primarily scholarly and

relate to the research

focus but somewhat

tangentially.

 Does not cite sources.

 Sources are

disproportionately non-

scholarly and do not

clearly relate to the

research focus.

Spelling &

Grammar

 No spelling & grammar

mistakes

 Minimal spelling &

grammar mistakes

 Noticeable spelling and

grammar mistakes

 Excessive spelling

and/or grammar

mistakes

Manuscript

Format

 Title page has proper

APA formatting

 Used correct headings &

subheadings

consistently

 Title page

approximates APA

formatting

 Used correct headings

& subheadings almost

consistently

 Title page deviates a bit

more from APA

formatting

 Headings & subheadings

less consistent

 Title page completely

deviates from APA

formatting

 Headings and

subheadings completely

deviate from suggested

formatting or are

absent altogether

Additional Comments:

Swygart-Hobaugh, A. J. (Some elements adapted from vom Saal, F., “Scoring Rubric—Scientific Paper”

http://www.biology.missouri.edu/courses/Bio4984_vomSaal/pdf/Sci_Paper_Critique.pdf and Cornell College/Colorado College., “Figure 1:

Research Paper Rubric” http://www.coloradocollege.edu/library/acmassign/tools.html

Statistics homework help

Systems Engineering & Voice
of the Customer

US Automotive Recalls
Vehicle Sold

(Millions) Vehicles Recalled

2011 2012 2013 2011 2012 2013

Toyota 1.6 1.7 2.2 219% 312% 241%

Honda 1.2 1.4 1.5 325% 243% 187%

BMW 0.2 0.3 0.3 150% 200% 300%

Hyundai 1.1 1.3 1.3 109% 138% 169%

Chrysler 1.4 1.4 1.8 57% 76% 261%

Ford 2.1 2.2 2.5 157% 64% 48%

Nissan 1.0 1.0 0.9 30% 100% 133%

GM 2.5 2.6 2.8 68% 58% 54%

Slide 2

System understanding

HoQ1→Boundary→HoQ2→P-diagram→DFMEA→PFMEA→SCIF→Control plan

HoQ1→Boundary→HoQ2→P-diagram→DFMEA→PFMEA→SCIF→Control plan

HoQ1→Boundary→HoQ2→P-diagram→DFMEA→PFMEA→SCIF→Control plan

HoQ1→Boundary→HoQ2→P-diagram→DFMEA→PFMEA→SCIF→Control plan

System validation plan

System verification plan

Sub-system verification plan

Component verification plan

Time line

System

Sub-
system

Component

System

Sub-
system

Requirements Flow Down Example

We Must Know the
Mathematical Relationship to
Flow Down Requirements
• What are the options if the engineering is not

known?
• Safety factor

• Pass responsibility to customer

• Refuse the business

• Increase price to compensate for the additional risk

• Use experiments to create empirical models

• Basic research

Never accept a known risk for safety or compliance with
government regulations

Slide 6

Relationships

Boundary
diagram

Parameter
diagram

Design
FMEA

R&R
matrix

HoQ #1

Process
FMEA

Critical
characteristics
identification
form

Manufacturing
control plan

Field
performance

Project goals Knowledge storage & re-use is

critical

Our Influence Over Risk

Start

up

RISK MANAGEMENT PROCESS

(APQP)

ABILITY TO
INFLUENCE RISK

Design &

Develop

Product

Design &

Develop

Process

Product &

Process

Validation

RISK

Start

up

RISK MANAGEMENT PROCESS

(APQP)

ABILITY TO
INFLUENCE RISK

Design &

Develop

Product

Design &

Develop

Process

Product &

Process

Validation

RISK

Time
Start

up

RISK MANAGEMENT PROCESS

(APQP)

ABILITY TO
INFLUENCE RISK

Design &

Develop

Product

Design &

Develop

Process

Product &

Process

Validation

RISK

Start

up

RISK MANAGEMENT PROCESS

(APQP)

ABILITY TO
INFLUENCE RISK

Design &

Develop

Product

Design &

Develop

Process

Product &

Process

Validation

RISK

Time

DEFINE IT RIGHT

House of Quality (HoQ)
• Features:

• Inputs from customer

• Measurable functional requirements to
test against

• Targets and limits set by customer

• We will use rooms 1 and 3 to assist in
creating the FMEA

• May be:
• Used as an aid when completing a CSCM or

• Not used if the CSCM is sufficient in define
customer needs

7

3

5

4

6

2

8

Direction of improvement

Calculated
importance

Competitive
comparison of

customer
ratings

Conflicts

Correlations

Competitive
benchmarks

Targets
and limits

Functional requirements

1

C
u

st
o

m
e

r
e

x
p

e
ct

a
ti

o
n

s

Fast Car Example

91 3 9

Types of Requirements
• Functional Requirements

• Define what functions need to be done to accomplish the mission objectives
• Example

• The Thrust Vector Controller (TVC) shall provide vehicle control about the pitch and yaw axes.

• This statement describes a high level function that the TVC must perform.

• Statement has form of Actor – Action Verb – object acted on

• Performance Requirements (Specification)
• Define how well the system needs to perform the functions
• Example: The TVC shall gimbal the engine a maximum of 9 degrees, +/- 0.1 degree

• Constraints
• Requirements that cannot be traded off with respect to cost, schedule or performance
• Example: The TVC shall weigh less than 120 lbs.

• Interface Requirements
• Example: The TVC shall interface with the J-2X per conditions specified in the CxP 72262

Ares I US J-2X Interface Control Document, Section 3.4.3.

• Environmental requirements
• Example: The TVC shall use the vibroacoustic and shock [loads] defined in CxP 72169, Ares 1

Systems Vibroacoustic and Shock Environments Data Book in all design, analysis and testing
activities.

• Other -illities requirement types including availability, reliability, maintainability, etc.

Attributes of Acceptable Requirements
• A complete sentence with a single “shall” per numbered

statement

• Characteristics for Each Requirement Statement:
• Clear and consistent – readily understandable

• Correct – does not contain error of fact

• Feasible – can be satisfied within natural physical constraints,
state of the art technologies, and other project constraints

• Flexibility – Not stated as to how it is to be satisfied

• Without ambiguity – only one interpretation

• Singular – One actor-verb-object requirement

• Verify – can be proved at the level of the architecture applicable

• Characteristics for pairs and sets of Requirement Statements:
• Absence of redundancy – each requirement specified only once

• Consistency – terms used consistent

• Completeness – usable to form a set of “design-to” requirements

• Absence of conflicts – not in conflict with other requirements or
itself

• Clarified with boundary and P-diagrams

• NASA Systems Engineering Handbook for Reference

Requirements Definitions Mistakes
• Writing implementations (How) instead of

requirements (What)
• Forces the design

• Implies the requirement is covered

• Using incorrect terms
• Use “shall” for requirements

• Avoid
• “support”

• “but not limited to”

• “etc”

• “and/or”

• Using incorrect sentence structure or bad grammar

• Writing unverifiable requirements
• E.g., minimize, maximize, rapid, user-friendly, easy,

sufficient, adequate, quick

• Requirements only written for “first use”

Did any Changes or Improvements Have a Negative
Impact on Another Function?

Potato Cannon Exercise
• Customer wants to win the potato cannon contest

• Fire a potatoes into squares
• Square are 20 meters long on each side

• Center of square is 150 meters away

150 meters

10 meters

Potato Cannon
• How it works

• Potato is pushed into the sharpened barrel which cuts
potato to size

• Hair spray (propane – C3H8) is added at the back end

• Spark creates explosion

• Demonstration

• Components
• Loading rod

• Combustion Chamber, end cap, end cap connector and
igniter

• Barrel & reducer

• Teams of 3 or 4

• Use “TBD” if exact values
cannot be determined

• Additional Links
• Search for potato cannon fails

• Fire

Barrel

Combustion

Chamber

Igniter

Reducer

End Cap Connector
End Cap

Igniter

Seal

Scoping and Definition of Responsibility
• The customer needs a solution and is looking to SKF to deliver some functions

• To deliver the functions, we need clear definition of the functions, and detail
regarding the conditions our product is expected to work under
• The CSCM provides the function definitions

• The boundary diagram contains these functions and
• the operating conditions

• responsibility for each component

Our Solution

System Part 1 System Part 2

System Part 3

Condition 1

Condition 2

Condition n

Function 1

Function 2

Function p

Las Vegas High Roller

Las Vegas High Roller
• Multiple companies designing simultaneously

• Used the boundary diagram to:
• Understand the tolerances of all interfaces

and non-interfacing parts that potentially
impact the bearing

• Define loading
• Wind loads
• Seismic events

• Define bearing handling and installation

• This was challenging
• Strengthened hub design
• Changed spindle design
• Given responsibility for installation procedure

and equipment design
• Automatic lubrication
• Automatic Condition monitoring

Las Vegas High Roller Boundary Diagram

Spindle

Tapered

sleeve

Housing

Grease

Support

Legs

Brace

Leg

CablesRim

Mounting

ring
Cabin

Drive

system

Spherical

roller

bearing

Inputs

•Loads (Cable, wind, passengers)

•Contamination (dust, water)
Desired Outputs

•Fatigue life

•Wheel rotation

•Accommodate heat growth

Undesired Outputs

•Friction

•Vibration

Operating conditions analyzed:

– Service case 1

– Service case 2

– Service case 3

– Service case 4

DESIGN IT RIGHT

What Could Go Wrong?
• Now the boundary of our solution is clearly defined, we should

question what could cause the functions not to be delivered.

• Our solution will work and be used in some uncontrolled

conditions. These external factors are called noise factors.

• The standards define 5 types of noise factors:

• Piece to piece variation (tolerance stack-ups)

• Degradation over time

• Environment

• Customer use and abuse

• System interaction

• Listing these potential noise factors is key, as these noise factor will

become the potential causes of failure.

Unintended Functions
• Unintended Failures

• Electric car burns down garage (Alleged)

• “Toyota announced it was recalling 7.4 million vehicles to repair power-window switches
that can break down and pose a fire risk”

• Sooner or later everything will fail
• 100 year old car

• Modified car (Pimp my Ride)

• How is a car’s brake system designed to fail safe?

• The DFMEA should be used to
• Anticipate failures and ensure failures are as benign as possible

• Limp home mode in a vehicle

• Assure no injuries

• Boeing considered encapsulating dreamliner batteries in fire proof container

• Explore and eliminate unintended failure modes

• Other unintended failures
• Scully

• McDonnel Douglas

Foreseeable Use & Abuse

Potential Causes
• Potential causes of failure are taken from the P-

diagram

• The engineer is NEVER the failure cause; examples
• Wrong bolt plating specified

• Lower plating thickness is incorrect

• In identifying potential causes of failure, use concise
descriptions of the specific causes of failures
• Bolt plating allows rusting from exposure to humidity

• Potential cause of failure is defined as an indication
of how the design or process could allow the failure
to occur, described in terms of
• Something that can be corrected or can be controlled

• Something remedial action can be aimed at

• Something that can be identified as a root cause

• The system allowed or even facilitated the failure
cause – the system must be changed

Failure Modes
• How can the function not be

delivered?

• There are 4 potential failure modes:
• No function at all

• Intermittent function

• Degradation of performance

• Unintended function

Identification of Potentially Special Characteristics
• Utilize two stages of special characteristics

• Potential
• Confirmed

• Potential special characteristics are identified by
• Design – as a rule-of-thumb 80% of all variation

• Cannon animation
• Reservoir example

• ISO or other standard
• Customer
• Supplier

• Potential special characteristics are identified on the drawing and SCIF
• Manufacturing (or the supplier) confirms if special controls are needed

for these characteristics based on capability (including special causes)
• There is no set capability limit
• Maintain flexibility based on severity and industry

• The SCIF records the confirmation decision and reasoning
• The decision is reviewed as part of the ECM process

Solution Space for Projectile Distance
• Solution 1

• Angle 70°± 1°

• Velocity 316.5 ± 1 ft/sec

• Solution 2

• Angle 70°± 0.8°

• Velocity 316.5 ± 2.5
ft/sec

• Solution 3

• Angle 45°± 1°

• Velocity 253.8± 6.2
ft/sec

• Solution 4

• Angle 45°± 2°

• Velocity 253.8± 6.0
ft/sec

• Solution 5

• Angle 45°± 5°

• Velocity 253.8± 4.5
ft/sec

2100 ft

1900 ft

2000 ft

Gearbox Example

Only one special

characteristic

Airbus Super Puma Crash
• What items should be added to the

P-diagram?
• Customer use & abuse (Dropped

gearbox)
• This has been moved to the boundary

diagram

• Piece-to-piece (worst case roller &
raceway profiles)

• What is the failure cause?
• Worst case roller & raceway profiles &

max shock load

• The accident could have been
prevented if there was a warning
• Detection of a metal particle
• Vibration

Video

Failure Effect
• The effects should always be stated in terms of the

specific project, system, product or process analyzed​

• Remember that a hierarchical relationship exists
between the component, sub-system, and system levels.
For example, a part could fracture, which may cause the
assembly to vibrate, resulting in an intermittent system
operation.

• Do not list effect beyond your area of responsibility​

• Brake tube designer cannot have “No Brakes” as effect​

• The effect is “Loss of Brake Pressure”​

• State clearly if the failure mode could impact safety,
non-compliance to regulations

Severity
• Severity is defined as how serious the effects of a failure

would be should they occur

• It is important to realize that each failure mode may have
more than one effect, and each effect can have a different
level of severity

• It is the effect which is being rated and not the failure,
therefore each effect should be assigned its own severity
ranking

• A scaling system from 1 to 10 should be used, with 10 being
reserved for the most severe failure modes

• You may have to defer to the customer
• Build to print PFMEA with no access to DFMEA

Is the Product Designed Right?

• Green specifications – provide the customer’s
functions

• Blue specifications – artificially tight providing a
safety factor
• Improperly built parts may deliver the customer’s functions

• Red specifications – the design is not correct
• Properly produced parts will not always deliver the

customer’s functions

What Happens if You Drive Off with the Gas
Pump Nozzle Still in the Car?

• This should be on the P-diagram
• Customer use (and mis-use)

• What was the severity of this incident in 1950?

• What is the severity of this incident today?
• The hose that attaches the nozzle to the gas pump is designed to break into two

pieces when a certain amount of force is applied to it

• Next time you’re at the gas station, check the hose for a metal coupling

• That’s the break-away point

• Once the hose is broken and you’re off on your merry way, check valves in the
hose keep fuel from leaking out and creating a hazard

• Severity can only be improved by a design change
• Failure mode designed out

• This is the design control

• It is important to keep this information in the DFMEA so future designs don’t
repeat the mistake
• Remove the coupling for cost save

• Remove check valves for cost save

What Happens if You Drive Off with the Gas
Pump Nozzle Still in the Car?

Controls
• There are two types of design controls to consider

• Prevention controls
• Aim to eliminate or prevent the cause of the failure mechanism or the failure mode from

occurring

• Aim to reduce rate of occurrence

• The preferred approach is to use prevention controls
• Gives a more robust product or process

• Initial occurrence rankings will be affected by the prevention controls

• Prevention controls
• Predict performance based on scientific knowledge or

• Ensures performance based on historical experience

• Design out failure mode

• Examples of prevention controls
• Fail-safe designs (if two wheel speed sensors disagree, the ABS system is disabled)

• Follow proven design and material standards (internal and external)

• Calculation & Simulation studies (computing the maximum deflection by computing deflection for
every possible combination of tolerances)

• Use of components proven under less stressful conditions

• Error-proofing (using non-symmetrical parts to make it impossible to install a component backwards)

Controls
• Detection controls

• Aims to identify the existence of a cause that results in a mechanism of
failure

• The detection ranking is associated with the best detection control listed
in the current design control detection column

• Should include identification of those activities which detect the failure
mode as well as those that detect the cause, and could include:
• Prototype testing

• Validation testing

• Design of experiments including reliability testing

• Mock-up using similar parts

• A suggested approach to current design control detection is to assume
the failure has occurred and then assess the capabilities of the current
design controls to detect this failure mode

• Warning
• Often the detection method is assumed to be good because no parts with

the failure mode have passed through the detection method

How Much Confidence Do You Have?
• Compare this to a design change, or

a choice between two materials
• Is George Bush equivalent to the

university player?

• They are both one-for-one (the same
performance)

• What should be considered for a DV
test
• Choose parts and loads that target the

highest risk areas
• Minimum thickness

• Highest wavieness

• Maximum preload

• Highest load, etc

Occurrence Rating

• The occurrence ranking is solely a function of prevention
controls

• No prevention control gives a ranking of 10

• Ranking of 1
• DFMEA: perfect knowledge of engineering with calculations at worst

case

• PFMEA: perfect error proofing or PPM less than 1

• This forces a separation of the prevention and detection
controls and strengthens the thinking of prevention over
detection

• Ideally, prevention=1 and detection=10

• Weaker prevention mandates stronger detection

Detection Rating
• The detection rating is determined by how well a test

can discover the failure mode or effect

• The rating is dependent on:
• The correlation of the test to real world conditions

• The parts tested
• If parts built very close to nominal are tested, the detection test

provides little value

• The best test utilizes parts built close to the worst case condition that
aggravates the failure mode or effected targeted

Priorities
• Severity is the primary driver

• Action Priority (AP)
• Low, Medium or high based on a combination of severity, occurrence

and detection

• Risk Priority Number (RPN)
• This is calculated by multiplying the 3 rankings recorded for severity,

occurrence and detection
RPN = Severity (S) * Occurrence (O) * Detection (D)

• RPN can range between 1 and 1000

• The use of an RPN threshold is NOT a recommended practice for
determining the need for actions
• Establishing such thresholds may promote wrong behavior (trying to justify

a lower occurrence or detection ranking value to reduce the RPN)

• This type of behavior avoids addressing the real problem that underlies the
cause of the failure mode and merely keeps the RPN below the threshold

• IF customers require actions based on thresholds, we shall follow the
customer requirements

AP

Recommended Actions

• The intent of recommended actions is to improve
the design

• Identifying these actions should consider reducing
rankings in the following order:
• Severity

• Occurrence

• Detection

• Be sure to include any actions that may be the
responsibility of the customer

• Never list a recommended action without a
completion date and responsibility for actions
related to safety or adherence to government
regulation

Robust Design Example
Cost was

reduced by

32% while

the process

capability

was

increased by

132%

BUILD IT RIGHT

The Transition from the DFMEA to the PFMEA
• The drawing has so many characteristics … how do I control them all?

• When creating the DFMEA, the characteristics with the biggest impact and
severity on the functions to be delivered were identified as potentially
special characteristics

• Other characteristics must also be controlled, but the consequences of the
non-special characteristics does not warrant the level of oversight that
must be taken with special characteristics

• Special characteristics are only potential at the design phase;
manufacturing may have error proofing or outstanding capability, that
eliminates any need for special controls

The Transition from the DFMEA to the PFMEA

• The Special Characteristics Information Form (SCIF) lists all the potentially
special characteristics from the DFMEA, eliminating the possibility of
overlooking a potentially special characteristic

• The SCIF also records the origin of the characteristic
• Was the characteristic determined from an engineering calculation?

• Was the characteristic flowed down by our customer?

• Was the characteristic flowed up by a supplier?

• Is the characteristic required by a standard?

• The SCIF also records why each characteristic was confirmed or not, and
what controls are in place for those characteristics confirmed

Transition to the PFMEA with the SCIF
• Forms the bridge from the DFMEA to the PFMEA

• Prevents Special Characteristics from being misses

Internal

PFMEA
• What do we have now :

• The specifications for all characteristics

• Potentially special

• Not potentially special

• Now we have to determine how to build the product to specification

• We have the requirements for the final part

• What are the requirements for the intermediate steps?

• What are the requirements for purchased material?

• How do we ensure purchased material conforms to our specifications?

Product Flow

• Just like functions are flowed down from the end
customer to sub-systems and eventually components,
the manufacturing characteristics needed to deliver
these functions are flowed back from the final assembly
to previous manufacturing steps and eventually
purchased materials

• The inputs for each step are the required outputs for
the previous step

What Could Go Wrong?
• Now the boundary for each manufacturing step is clearly defined, we should question what could

cause the characteristics not to be achieved.

• There are only 4 potential failure modes:
• No characteristic (part not hardened)
• Characteristic not achieved for the entire part (roughness is OK for 90% of the raceway, but

not the remaining 10%)
• Degradation of performance (part is hardened, but not to specification)
• Unintended function (part is scratched)

• There is variability in manufacturing. This variability is defined by noise factors.

• The standards define 5 types of noise factors:
• Man
• Machine
• Material
• Measurement
• Environment

• Listing these potential noise factors is key, as these noise factor will become the potential causes of
failure.

People are not the Problem
• The system is always at fault

• Do not blame the operator

• Do not blame the engineer

• Root cause is found by determining how the system allowed a
defect to be created and escape

• Example
• The label is placed in an incorrect position on a box

• 8D corrective action – the operator was sent to training

• Noooooooooooooo!

• Why did the system allow the operator to incorrectly place the label?
• No orientating fixture?

• Poor light?

• What can be done to prevent an operator from locating the label incorrectly?

What Happens if the Characteristics are not Delivered

• If a special characteristic is produced outside the green
specification, it does not matter if design determined the
specification wrong, or if the part was produced wrong, the
result is the same

• This must be reflected in the PFMEA; the severity and the
effect in the PFMEA must be the same as in the DFMEA

• The PFMEA also includes an internal severity ranking
• Is there a possibility of injury?

• What is the severity of finding a defect at the final production step
as opposed to immediately detecting the defect?

DFMEA & PFMEA

• If the failure mode, severity or effect is updated in the DFMEA, the PFMEA must
also be updated

Can we Build the Part to Specification

• How strong is our manufacturing knowledge?
• Can I predict the process outputs from inputs

(machine settings)?

• Is my SOP reliable given the input conditions
specified on the boundary diagram?

• Are error proofing methods in use, and how
effective are they?

• This ability to predict function performance
provides a probability of the failure to produce
the part to specification, and is assessed with
the Occurrence rating

Why Occurrence Does Not Come From Defect Data

• Green specifications – provide the customer’s
functions

• Blue specifications – artificially tight providing
a safety factor
• Improperly built parts may deliver the customer’s

functions

• Red specifications – the design is not correct
• Properly produced parts will not always deliver the

customer’s functions

• Case 1
• Red specifications, but Cpk

is very good, and all
production is within the
blue lines

• DFMEA occurrence should
be high, and PFMEA
Occurrence should be low

• Case 2
• Blue specifications, and

Cpk is poor resulting
production between
Green and Blue

• DFMEA occurrence should
be low, and PFMEA
Occurrence should be high

Can We Build the Part to Specification?

• How strong is our assessment program?
• Are all characteristics measured?

• Are characteristics measures at a rate of 100% of
sampled?

• How much measurement error is present?

• Has gage R&r been removed from the specifications?

• How often are known good and known bad parts
measured?

• Are statistical process control or trend charts used?

• This ability to measure characteristics provides a
probability of our ability to detect the failure of our
manufacturing process to deliver the required
characteristics, and is assessed with the Detection
rating

Purchased Material

• Receiving is a process

• What are the requirements?

• What are the controls?
• Prevention

• Supplier certification

• Supplier audits

• Require supplier to send data with each shipment

• Electronic access to supplier data

• Detection
• Incoming inspection

Manufacturing Control Plan
• The controls in the PFMEA become the Manufacturing Control Plan
• Additional information in the control plan

• Measurement assurance activities
• Reaction plans

• Following the Manufacturing Control Plan does not ensure zero defects
• The occurrence and detection rankings determine the effectiveness of

the manufacturing controls
• The effectiveness of the manufacturing controls combined with the

severity ranking highlights internal and external quality risks
• Highlighting these risks is a key part of business and technical gate

reviews
• The recommended actions portion of the PFMEA provides options for

mitigating these risks

Statistics homework help

Continuous Distributions

Normal Distribution

40%

30%

20%

10%

0%

  +   + 2  + 3 –  – 2 – 3

68%

95%

99.73%

50%

f x
x

( ) exp= −
−







1

2

1

2

2

 

There is no closed solution for the
integral of the normal probability
density function.

The standard normal random deviate
(z) was introduced to allow
integration via tables

• Mean of z =0
• STS of z = 1

This is no longer relevant, but the
term z is still used

z
x

=
− 

Normal Parameter Estimation

 = = =

x

x

n

i

i

n

1

( )

( )
 = =

=


s

x x

n

i

i

n
2

1

1


( )

 = =




= =

 
s

n x x

n n

i

i

n

i

i

n
2

1 1

2

1

Requires only a
single pass for
computer code

Normal Distribution

Properties:

1.Symmetrical

2.Measures of central tendency are all identical

(mean, median, mode, and midrange)

Central Limit Theorem
• Sums & averages become

Normal

• Y = x1 + x2 + … + xn

• Y = (x1 + x2 + … + xn)/n

• Regardless of the
distribution of the
individuals

• Excel Example

Lognormal Distribution

• If a data set is known to
follow a lognormal
distribution, transforming
the data by taking a
logarithm yields a data set
that is normally
distributed.

• Limited to right skewed
data









 −
−=

2
ln

2

1
e xp

2

1
)(



x

x
xf

Lognormal Data Normal Data

12 ln(12)

16 ln(16)

28 ln(28)

48 ln(48)

87 ln(87)

143 ln(143)

Lognormal Distribution

• Y = (x1)(x2) … (xn)

• ln(Y) = ln(x1) + ln(x2) + … + ln(xn)

• When a system is the result of multiplication or division
the result tends to be lognormal

• Lognormal distribution in engineering

• Ideal gas law

• Salt in a tank with flow & mixing

• Electrical field (coaxial capacitor)

Lognormal Distribution

nR

PV
T =

V

tf

dVeQ

= V
tf

dVeQ

=

r

Aa
E

2
=

Lognormal Probability Density Function

0 2 4 6 8
0

0.1

0.2

0.3

0.4

0.5

0.6

x

f(x)

=

=
=

=

=

=

Weibull Probability Density Function

• b = shape parameter

• q = scale parameter

• d = location parameter











=

− b

b

b

dqdq

b xx
xf e xp

)(
)(

1

0

0

X

f(x)
b=

b=

b=

b=

b=

q

Effects of the Shape Parameter

Effects of the Scale Parameter

0 5 10 15 20 25
0

0.02

0.04

0.06

0.08

0 50 100 150 200 250
0

0.002

0.004

0.006

0.008

q = 10

q = 100

0 50 100 150 200 250 300 350
0

0.002

0.004

0.006

0.008

Effects of the Location Parameter

d = 100

Weibull F(x) & R(x)

b

q

d



 −

−=

x

exF 1)(
b

q

d



 −

=

x

exR )(

Bathtub curve

• The bathtub curve is widely used in reliability engineering. It describes a particular form of the
hazard function which comprises three parts:

• “infant mortality”

• “useful life”

• “wear out”

• The bathtub curve is generated by mapping the rate of early “infant mortality” failures when first
introduced, the rate of random failures with constant failure rate during its “useful life”, and
finally the rate of “wear out” failures as the product exceeds its design lifetime.

• h(t) – Hazard function

Weibull slope
Shape parameter

• β < 1Failure rate decreases with operating time
Products having defects emanating from manufacturing, storing or mounting are screened
out at an early stage.

• β = 1Failure rate is constant
No memory of previous stress history, i.e. an old, still running product may be as good as a
fresh one.

• β > 1Failure rate increases with operating time
Process indicates deterioration of material properties (structure).

Bathtub curve

h(L)

Life (time)

β < 1 β = 1 β > 1

Early “infant
mortality”
failures Wear out

failures

Decreasing
failure rate

Constant
failure rate

Increasing
failure rate

Fa
il

u
re

r
a

te

Normal life

Weibull Hazard function

X

h(x)

b = 0.5

b = 1

b = 2

b = 3.6 b = 9

1/q

h(t) – Hazard function
• Instantaneous failure rate

• A measure of proneness to failure as a function of the age of units

Extreme values

Time to Fail
48

Time to Fail
15

Time to Fail
97

The system fails when one of the 3
components fail. What is the
system time to fail?

The system fails when all of the 3
components fail. What is the
system time to fail?

Exponential distribution

• Constant failure rate

• Lack of memory
• R(t2\t1)=R(t2)/R(t1)

• Example

• If x is exponential then 1/x is Poisson

Estimating Lognormal Parameters

Estimating Weibull Parameters

Statistics homework help

Study on Time Delay Analysis for Construction

Project Delay Analysis

Ar. Meena. V
M.Arch, Architecture department

Sathyabama University

Chennai, India

Ar. K. Suresh Babu

Associate Professor, Architecture department

Sathyabama University

Chennai, India

Abstract— Time delay is one of the biggest problems facing in
many construction buildings in India. Completing projects on

time is the key factor of the project, but the construction process

is subject to many variables and unpredictable factors, which

result from many sources such as availability of resources,

external factors, performance of parties and type of building. If

there is a delay in project it leads to loss of productivity,

increased cost, contract termination and disputes between

contractor and owner. The aim of this project is to examine the

causes and effects of delay on building construction project

during construction phase and to provide control measures for

time overrun in the project. A study carried out on construction

schedule delays and various delay analysis techniques and

methods in order to evaluate the causes of delay and their

impacts in the construction project. Then a questionnaire survey

is done to find the major causes of delay faced by Client,

Contractor, Consultant and Project manager. Population

sample of 35 was used in which 30 was deployed. From the

survey and study identified 67 causes of delay under 9 major

groups such as Project team, Owner, Contractor, Consultant,

Architect, material, labour, equipment and external factors.

Then a ranking method is done based on relative importance

index method to find major cause of delay. It is found that the

most common factors of delay which is repeated in most of the

project are lack of funds to finance the project to completion,

labour shortage, material shortage, lack of effective

communication, lack of supervision and changes in drawings.

The outcome of the project is to provide recommendation to

control delay in the project during construction phase.

Keywords— Delay analysis technique, causes of delay, tools

to evaluate delay in construction, delay control measure

INTRODUCTION

In construction, delay could be defined as the time overrun

either beyond completion date specified in a contract or

beyond the date that the parties agreed upon for delivery of a

project. It is a project slipping over its planned schedule. The

delay in the project has an adverse effect on project success

in terms of time, cost and quality. The objective of the project

is
• To identify delay factors in construction projects

• To rank the delay factors according to the importance
level on delays in project

•To find the tools to analysis and evaluate the time delay
factors in the construction building.

•Recommendations to control delay during construction
phase for construction project

I. STUDY ON DELAY ANALYSIS

A. Construction project planning

Planning explains “what” is going to be done, “how”,

“where”, by “whom”, and “when” for effective monitoring

and control of complex projects. The objective of project

planning is to complete the construction within the specified

time and budget. In construction project planning the steps

need to be identified are as follows.

•Feasibility of the project

•Project management plan

•Identifying the constraints in the project (time, cost,

resources)

•Project delivery method, stakeholders, funding sources

•Construction method

•Identifying risk in project

•Milestone, duration and budget

•Roles and responsibility

•Preparation of contract documentation

B. Project scheduling

Project scheduling covers only the issue of when? i.e. when

works need to be done and completed. By doing project

scheduling it helps to control and measure the project

duration and provides information for timely decisions to be

taken when there is a change in schedule. The results of doing

a detailed project schedule are duration of the project and

completion date can be easily tracked, helps to calculates the

start or end of a specific activity, evaluate the effect of

changes, improves work efficiency, predict and calculate the

cash flow, resolve delay claims and it serves as an effective

project control tool

C. Types of project scheduling

Selection of the most appropriate scheduling technique

depends on the size and complexity of the construction

Project, the preferences of the entity preparing the schedule,

and the scheduling requirements of the Contract. The most

common scheduling techniques used for construction projects

are Gantt Charts or bar charts, linear schedules, program

evaluation and review technique and Critical Path Method

(CPM) schedules.

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D. Progress monitoring

When updating a project, actual progress is recorded for

each activity relative to the date of each update. This regular

update will include progress on values for: dates on which

activities started or finished actual percent of work completed

within each task, actual resources expended on each task and

actual cost expended on each task. There are six basic

techniques for measuring the progress of a task in a CPM

network as follows: Unit Measure, Incremental Milestones,

Start/finish, Observational Assessment, Level of Effort/Cost

Ratio and Equivalent Units

E. Classification of construction delays

The classification of delays is dependent upon the type

and magnitude of the effect that an activity will have on the

project and who is responsible for the delay among the stake

holders. Hence they are classified into four categories such as

Critical or noncritical, Excusable or non-excusable,

Compensable or Non-compensable and Concurrent or Non-

concurrent.

Critical Versus Non-Critical Delays

The delays that affect the project completion time or date are

considered as critical delays. And the delays that do not affect

the project completion time or date are noncritical delays. If

certain activities are delayed in the construction project life

cycle, the project completion date will be delayed. The

determining which activities truly control the project

completion date depends on the following: The project itself,

the contractor„s plan and schedule (particularly the critical

path), the requirement of the contract for sequence and

phasing and the physical constraint of the project.

Excusable and Non-Excusable Delays

Delay that is due to an unforeseeable event beyond the

contractor„s or the subcontractor„s control. Normally, based

on common general provisions in public agency

specifications, delays resulting from the following events

would be considered excusable: General labor strikes, fires,

floods, act of God, owner-directed changes, errors and

omissions in the plans and specifications, differing site

conditions or concealed conditions, unusually severe weather

Non-excusable delays are events that are within the

contractor„s control or that are foreseeable. These are some

examples or non-excusable delays: Late performance of sub-

contractors, untimely performance by suppliers, faulty

workmanship by the contractor or subcontractors, a

project-specific labor strike caused by either the

contractor„s unwillingness to meet with labor

representative or by unfair labor practice

Compensable and Non-Compensable Delays

Compensable delay is caused by the owner or the owner’s

agents. A compensable delay is a delay where the contractor

is entitled to a time extension and to additional compensation

such as payment for the delay.

Non-compensable delay is caused by third parties or incidents

beyond the control of both the owner and the contractor

where the contractor is normally entitled to a time extension

but no compensation for delay damages

Concurrent or Non-concurrent.

Concurrent delays are two or more parallel and independent

delays to the critical path of a project. Concurrent delays can

be on the same critical path or on a parallel critical path

F. Delay Analysis Techniques

Delay analysis is a analytical process that should be

employed with project documentation along with collected

data from project site. The selection of delay analysis

depends on the variety of factors and the available records.

There are five commonly used delay techniques.

1. Impacted as-planned method

2. Time impact analysis method

3. Collapsed as-built or but-for analysis method

4. Windows analysis method

5. As-planned versus as-built (Total time) method

Impacted as-planned method

According to Trauner et al. (2009), in this method the analyst

specifies the as planned schedule, and inserts into this

schedule the changes which caused project delays. These

changes are the only determined delays recorded during

construction process which may have affected the project

duration. Trauner et al. (2009) point out the major

weaknesses of this method as it does not reflect the dynamic

nature of construction project and the critical path.

Time impact analysis method

The analyst determines the amount of project delay

resulted from each of the delaying activity successively by

calculating the difference between the project completion

date of the schedule after the addition of each delay and

that prior to the addition (Ndekugri, Braimah, and

Gameson, 2008).

Collapsed as-built or ‗ ‘but-for’ analysis method

In this method, the analyst studies all contemporaneous

project documentation and prepares a detailed as-built

schedule instead of an as-planned schedule as mentioned in

the what-if method. The analyst subtracts or removes

activities which affected the project from the as-built

schedule (Trauner et al. 2009).

Windows analysis method

Window analysis method is also called the contemporaneous

period analysis and snapshot method. In this method, the

basic concept is that the total project duration of CPM

schedule is divided into digestible time periods or windows

(e.g., monthly) and the delays that occurred in each windows

of time are analyzed successively by focusing on the critical

paths (Hegazy and Zhang, 2005).

As-planned versus as-built (Total time) method

Basically, the main concept is that the as-planned versus

as-built method compares two schedules, which is why it is

also called “the total time method or net impact method”.

In this method the assumption is that one party (contractor)

causes no delays and other party (owner) causes all

delays.

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G. Programme updates

It is used to document the performance of the employer,

the professional team, designers, and the contractor and their

ability to meet commitment dates. Programmes are updated

to communicate actual project status from time to time, keep

the programme relevant as a useful management tool, record

actual performance of all parties‟ alike, record changes to the

original plan and support forensic or prospective delay

analysis. When no frequency is specified, it is unlikely that a

contractor will submit updated CPMs to the employer until

extensions of time are granted or significant changes to scope

or sequence are incorporated into the project. The minimum

data required to properly update a programme would be

percentage complete, remaining duration (%), actual start,

and actual finish.

H. Records

Once the program update is done then changes need to be

recorded. When good record keeping procedures are

established and maintained, contract administrators are often

able to access key information quickly and in a timely enough

manner to respond to crises and manage problems at the time

they arise. Many standard forms require contractors to

provide notice of an intention to make a claim for time and/or

money within a reasonable time after the event which gave

rise to the claim. Records can be inspected by the employer‟s

representative from time to time. For each delay event an

„event analysis‟ needs to be done.

II. QUESTIONNAIRE SURVEY

The Survey is designed based on the objective of the study
to find out the causes of delays in construction projects

and effect of the delays on overall project. The Survey

is framed in such a way that the personal view of

different people involved in different projects (Architect,

Consultant, Owner, Project manager, Contractor) is

collected and analyzed. This questionnaire consists of 63

causes of delay on which a detailed analysis will be carried

out by using statistical concept. These causes are classified

into nine groups according to the sources of delay: Factors

related to Project, Owner, Contractor, Consultant,

Architect/design-team, materials, equipment, manpower

(labor), and external factors.

A. Questionnaire format

Respondents are asked to fill What is the frequency of

occurrence for this cause?. The frequency of occurrence was

categorized as follows: always, often, sometimes and rarely

(on 4 to 1 point scale). Respondents are required to fill the

respective places with only scale points (1, 2, 3 and 4) of their

opinion.

Frequency of Occurrence

Always (4): Generally occurs in all the projects (70%-100%).

Often (3): Occurs in 5 to 7 projects out of 10 projects (50%-

70%).

Sometimes (2): Occurs in 1 to 5 projects out of 10 projects

(10%-50%).

Rarely (1): Occurs only 1 time out of 10 projects (>10%).

The questionnaire format is provided in appendix

B. Respondent’s profile

The questionnaires were distributed to Owners, Project

Manager, Architect, Consultants and Contractors of Indian

construction industry. The respondents involved in the

survey had several years of experience in handling various

types of projects. The characteristics of the respondents

participated in survey are summarized below. Population

sample of 35 was used in this survey. A total sample of 31

was deployed.

Fig. 1. Result of respodents

Fig. 2. Working experience

III. QUESTIONNARIE SURVEY RESULTS

The collected responses from different categories of people

involved in construction project gives the major causes of

delay factor faced in the construction process. The mean of

each group of question is calculated using Relative

Importance Index to calculate the ranking and the percentage

of delay cause in the building. The final result showing the

contribution of different factors on the delay of a construction

project is shown below

0
2

4
6

8
10

Result of respondents

0

10

20

30

40

50

less than 10

years

11-15 years 16-20years 20 years and

above

working experience

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1078

TABLE I. RANKING FOR DELAY CAUSES

No Cause Of Delay Points Rank % Group

1 Very short original contract duration 20 17

Project

team

2 Legal disputes between parties 55 46

3

Inadequate definition of substantial

completion 50 42

4 Ineffective delay penalties 35 29

5 Types of construction contract 40 33

6 Types of project bidding 55 46

7 Payment delay 70 58

Owner

8 Delay in delivering the site 57 48

9 Change order 80 67

10 Late approval of design document 51 43

11 Late approval of sample material 54 45

12 Lack of communication 82 68

13 Late decision making 40 33

14 Conflicts between partners 30 25

15

Unavailability of incentives for contractor

for finishing ahead of schedule 45 38

16 Suspension of work 20 17

17 Financing difficulty 72 60

Contractor

18 Conflicts with sub-contractor 50 42

19 Rework 70 58

20 Poor site management and supervision 60 50

21

Poor coordination with labor and

subcontractor 65 54

22 Ineffective planning and scheduling 60 50

23 Improper construction method 40 33

24 Delay in sub-contractor work 45 38

25 Lack of knowledge 50 42

26 Frequent change of subcontractor 45 38

27 Poor qualification of technical staff 52 43

28 Site mobilization delay 52 43

29 Inspection and testing delays 52 43

Consultant

30 Approval delay 45 38

31 Poor communication 62 52

32 Conflict between consultant & architect 45 38

33 Lack of experience 45 38

34 Errors in design document 50 42

Architect

35 Delay in producing design documents 65 54

36 Inadequate details in drawing 51 43

37 Insufficient data collection & survey 45 38

38 Misunderstanding of owners requirement 45 38

39 Unused advanced design software 52 43

40 Shortage of material 70 58

Materials

41 Change in specification 60 50

42 Late delivery 65 54

43 Damaged of required material 45 38

44 Delay in manufacturing 54 45

45 Late procurement 60 50

46 Lack of material availability 54 45

47 Shortage of equipment 61 51

Equipment

48 Equipment break down 62 52

49 Poor operator skill 50 42

50 Low productivity & efficiency 52 43

51 Lack of high technology equipment 65 54

52 Shortage of labor 71 59

Labor

53 Personal conflicts 50 42

54 Lack of knowledge 60 50

55 Lack of communication 72 60

56 Lack of skilled labor 80 67

57 Poor soil condition 45 38

External

Factors

58 Delay in obtaining permits 76 63

59 Climatic factor 75 63

60 Unavailability of utilities 44 37

61 Accidents during construction 42 35

62 Changes in government regulation 65 54

63 Delay in final inspection 60 50

A. Highest percentage of delay group

From the above finding and analysis using ranking

method the group which is more responsible for the delay in

the project is find out. According to the survey result it is

found that resources are the main reason for the delay in the

project along with external factors it is then followed by

Contractor, then Owner and the others.

Fig. 3. Highest percentage of delay group

0 20 40 60 80

Project Group

Owner

Contractor

Consultant

Architect

Material

Equipment

Labor

External Factors

Points

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B. Template to evaluate time delay
The tools to evaluate and analysis time delay factors are CPM

and PERT. The collected data from the tools should be filled

in template for event analysis.

TABLE II. EVENT ANALYSIS SHEET

DESCRIPTION FORMULA VALUE

Planned quantity PQ

Planned duration PD

Planned productivity PP

Total budget TB

Cost per unit C TB/PQ

Actual quantity AQ

Actual duration AD

Actual productivity AP

Planned value PV, BCWS (AD*TB)/PD

Actual cost AC, ACWP C*AQ

Earned Value (EV) BCWP
EV = PV x(

AP/PP)

Cost Variance CV
EV-AC
(BCWP -ACWP)

Cost Variance % CV% CV/EV

Cost Performance

Indicator
CPI EV/AC

To Complete Cost

Performance Indicator
TCPI

(TB-EV)/(TB-

AC)

Schedule Variance SV
EV-PV

(BCWP- BCWS)

Schedule Variance % SV%
SV/PV

(SV/BCWS)

Schedule Performance

Indicator
SPI EV/PV

To Complete Schedule

Performance Indicator
TSPI

(TB-EV) / (TB –

PV)

Budget At Completion BAC = TB

Estimate At Completion EAC AC +(BAC- EV)

Variance At Completion VAC BAC – EAC

Planned % Completed PV / BAC

% Completed Actual AC / EAC

C. Recommendations

From the survey it is found that contractor has the highest

percentage of cause of delay followed by owner and then

consultant. So recommendation to control major causes of

delay are listed below

TABLE III. RECOMMENDATIONS FOR MAJOR CAUSES OF DELAY CAUSES

Causes of delay Recommendations

Weather

condition

Conducting detailed and perfect surveys towards

the field condition and previous weather data

External factors Monitor the work done by the earlier contractors to
make sure that delays outside your control are

recognized and documented.

Lack of funds Optimize cash flow in accordance with the

requirements and make sure fund needed for
project is available to execute the project

Deviation of

scheduling

Develop detailed and accurate schedule to

facilitate easy and controlled scheduled execution

Lack of
communication

Planning and applying Management Information
System(MIS)

Poor decision

making process

Conduct routine/regular coordination meeting and

develop a procedure regarding decision making.

Lack of

coordination /

Wrong
delegation of

authority

Develop a good, simple and easy to understand

system to regulate coordination procedures and

responsibility of units. Make organization chart
with detail job description which includes

responsibilities and roles of each function

Lack of

inspection

Provide separate technical staff or site manager for

periodic inspection and monitoring work process
which includes starting late, late submission of

drawings, mistakes or errors, resource availability,

etc. then proper record has to be maintained to
detect risk and mitigate.

Improper

planning

Understand the level of supply and demand to

produce detail planning and schedule.

Implement automatic machine work to avoid

shortage of labor such as automatic plastering

machine, wall painting, precast concrete wall, etc.

Lack of

knowledge

Contractor needs to aware of new technology and

techniques to reduce time duration for activity or

labor force

Lack of facilities

at site

Site management should be properly done to

ensure proper resource; basic facilities for worker

are available to increase productivity by doing

detail study in site condition.

Poor selection of

vendors

Consider supplier daily capacity and material

quality for selecting vendors to avoid delay and

conflicts.

Labor shortage Early workforce planning is essential for owners

and contractors to effectively manage project labor

risks. Then providing incentives/awards for

workers like best employer of the year/ month so

that productivity and quality of work will be

increased.

Skilled labor

shortage

Providing training and upgrade skills to use new

technology and techniques for unskilled labors to

increase productivity and efficiency of the worker.

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D. Conclusion

The major causes of delay which is found repeating in

almost every project are external factors, financial

difficulties, shortage of labor, insufficient labor productivity,

owner interference and improper planning. After analyzing

the data it is clear that the contribution of Contractor in

delay of the construction project is high then followed by

client then consultant side and others. Resource allocation is

the main criteria for doing schedule planning to allocate

duration for each activity included in the project so that delay

in the construction project can be reduced.

ACKNOWLEDGMENT (Heading 5)

I extend my gratitude to our Faculty Head Dr. A. Lilly
Rose, M. Arch., PhD, Head of the Department Dr. N.
Jothilakshmy, B. Arch; M.T.P., PhD, Assoc. Prof.T.Vennila
M.Arch, Mr.S.Kavin Kumar and Assoc. Prof. Ar. K. Suresh
Babu for their helpful suggestions and comments during my
project presentation. Mr.K.Gopala Krishnan, Mr.Karthik
Mohan, Mr.G.Hemanth kumar and my parents for their help
and support to complete the project.

REFERENCES

[1] Aditi Dinakar “Delay Analysis in Construction Project”, IJETAE, Vol.
4, No. 5, May 2014

[2] Aftab Hameed Memon, “Contractor Perspective On Time Overrun
Factors In Malaysian Construction Projects”, IJSET, Vol. 3, No. 3,
2014

[3] Ashwini Arun Salunkhe & Rahul S. Patil, “Effect of Construction
Delays on Project Time Overrun: Indian Scenario”, IJRET, eISSN:
2319-1163 | pISSN: 2321-7308

[4] “Construction Delay Analysis Methods”,
http://www.forensisgroup.com/expert-articles/construction-delay-
analysis-methods, 2013

[5] Roger Gibson “Construction delays: Extension of time and
prolongation claims”

[6] Desai Megha & Dr Bhatt Rajiv, “A Methodology For Ranking of
Causes of Delay For Residential Construction Projects In Indian
Context “, IJETAE, Vol. 3, No. 3, March 2013

[7] Enas Fathi Taher & R.K. Pandey, “Study of Delay in Project Planning
and Design Stage of Civil Engineering Projects”, IJEAT, Vol. 2, No.3,
February 2013

[8] Owolabi James D & *Amusan Lekan M. Oloke C., “Causes And Effect
of Delay on Project Construction Delivery Time” IJER, Vol. 2 No. 4
April 2014

[9] P. J. Keane & A. F. Caletka, “Delay Analysis in Construction
Contracts”, A John Wiley & Sons, Ltd., Publication 2008, United
Kingdom

[10] Songül Dayi “Schedule Delay Analysis In Construction Projects: A
Case Study Using Time Impact Analysis Method”, The Graduate
School Of Natural And Applied Sciences of middle East Technical
University, December 2010

[11] Theodore J. Trauner Jr., “Construction Delays: Understanding Them
Clearly, Analyzing Them Correctly”, 2009

APPENDIX

Name Date

Designation Location

Work Experience

Email Id

No Cause of delay

Alway

s Often

Some

times Rarely Group

1

Original contract
duration is too

short

Project

team

2
Legal disputes
between parties

3

Inadequate

definition of
substantial

completion

4

Ineffective delay

penalties

5

Types of

construction
contract

6

Type of project

bidding

7

Delay in progress

payment by owner

Owner

8

Delay to furnish
and deliver the

site to the

contractor by
owner

9

Change order

during

construction

1

0

Late in approval

design document

by owner

1

1

Delay in

approving shop
drawings and

sample material

1

2

Lack of

communication
between owner

and contractor

1
3

Slowness in

decision making
process

1
4

Conflicts between

joint ownership of
the project

1

5

Unavailability of

incentives for
contractor for

finishing ahead of

schedule

1
6

Suspension of
work by owner

1
7

Difficulties in

financing project
by contractor

Contra

ctor
1

8

Conflicts in

subcontractor

schedule in
execution of the

projec

Statistics homework help

Distribution Basics

Statistics

• Descriptive statistics – Those methods involving the collection, summarisation, presentation

and characterisation of a set of data in order to properly describe the various features of that

set of data.

• Inferential statistics – Those methods that make possible the estimation of a characteristic of

a population or the making of a decision concerning a population based only on a sample.

Population vs. sample

• A population is a total collection of observations or measurements of interest

• A sample is a subset of measurements or observations from a population

Sample vs. population

m = Population mean

s = Population standard
deviation

Estimate
Sample
statistics

Population
parameters

SAMPLE POPULATION

s = Sample standard
deviation (s)̂

X = Sample mean (m)̂

Describing the sample

• Central tendency – a distinct tendency to cluster about a central point (an average)

• Dispersion – amount of variation or spread in the data

• Shape – manner in which data are distributed

Statistical functions

• f(x) – Probability Density Function (PDF)

• Models a histogram

• F(x) – Cumulative Distribution Function (CDF)

• The area under f(x) to the left of x

• Probability of less than: integral of f(x) from negative infinity to x

• R(x) – Reliability function

• The area under f(x) to the right of x

• 1-F(x)

• Probability of greater than: integral of f(x) from x to infinity

• h(x) – Hazard function

• Instantaneous failure rate: f(x)/R(x)

• A measure of proneness to fail

Probability Density Function Definition

Symmetric vs. skewed data

• Mean > Median: Positive or right-skewness

• Mean = Median: Symmetry or zero-skewness

• Mean < Median: Negative or left-skewness

positively skewed (right) negatively skewed (left)

symmetric

Moment Generating Functions

1st moment generating function about the origin

2nd moment generating function about the mean

Skewness = the 3rd moment generating function
about the origin

Example
• Given the density function f(x) = ax, 0 < x < 10

• Determine the value of a that makes f(x) a valid density function

• Determine the mean and variance of the distribution

• Derive expressions for the reliability and hazard functions

( ) ( )( )ax dx
a

x
a

a
0

10
2

0

10

2 2
1

2
1

2
10 0 1

1

50
 =  =  − =  =

( )E x x
x

dx
x

dx( ) .= = = = 
50 50

1

150
10 6 667

0

10
2

3

0

10

( ) ( )V x x dx( ) . . .= − = − =
1

50
6 667

1

200
10 44 449 5 55

3 2 4

0

10

Example Continued

Probability Density Function (PDF)

0.59

0.71

0.83

0.95

1.07

1.19

1.31

1.43

1.55

1.67

1.79

1.91

2.03

2.15

2.27

2.39

2.51

2.63

0

10

20

30

40

Count

Probability Density Function

0

x

f(x)

a b

6 8
Diameter

4 6 8
0

0.2

0.4

0.6

0.8

1

Diameter

C
u

m
u

la
ti

ve
D

is
tr

ib
u

ti
o

n

4
0

0.002

0.004

0.006

0.008

P
ro

b
a

b
il

it
y

D
e

n
si

ty

Cumulative Distribution Function (CDF)

Reliability Function

0
x

1

F(x) R(x)

Hazard Function

• Instantaneous failure rate

Statistics homework help

Grading Guide

Note: Papers not turned in on or before the due date will lose one-half grade per day late–no exceptions.

A Paper: This paper does not just fulfill the assignment, it also has something original and important to say

and the points it makes are supported well. It is organized effectively, develops smoothly, and it is written

clearly and correctly. It is based on data or a review of the literature clearly related to the points it has to

make. The sources cited are authoritative, current, and appropriate in scope and quantity. Findings from the

literature are integrated into a readable essay. The conclusion suggests that the writer has synthesized the

literature, reflected on it and arrived at a position, stand or perspective on the topic. It is correct in mechanics

and APA citation style.

B Paper: This paper fulfills the assignment well. Its general idea is clear and it is effectively presented. It

handles its sources well, with no serious errors of fact or interpretation. It reports on adequate literature, but

sources are not as authoritative or current as they should be. Generally, the paper is correct in usage,

appropriate in style, and correct in mechanical standards of writing, including bibliographic citation.

C Paper: This paper is adequate to fulfill the assignment, but it might be better described as an annotated

bibliography. Points may be hard to follow and the paper may be poorly organized (e.g., unbroken narrative

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F Paper: This paper does not fulfill the assignment. It may omit important material lying within its declared

scope or make repeated errors of fact or interpretation.

Statistics homework help

Study on Time Delay Analysis for Construction

Project Delay Analysis

Ar. Meena. V
M.Arch, Architecture department

Sathyabama University

Chennai, India

Ar. K. Suresh Babu

Associate Professor, Architecture department

Sathyabama University

Chennai, India

Abstract— Time delay is one of the biggest problems facing in
many construction buildings in India. Completing projects on

time is the key factor of the project, but the construction process

is subject to many variables and unpredictable factors, which

result from many sources such as availability of resources,

external factors, performance of parties and type of building. If

there is a delay in project it leads to loss of productivity,

increased cost, contract termination and disputes between

contractor and owner. The aim of this project is to examine the

causes and effects of delay on building construction project

during construction phase and to provide control measures for

time overrun in the project. A study carried out on construction

schedule delays and various delay analysis techniques and

methods in order to evaluate the causes of delay and their

impacts in the construction project. Then a questionnaire survey

is done to find the major causes of delay faced by Client,

Contractor, Consultant and Project manager. Population

sample of 35 was used in which 30 was deployed. From the

survey and study identified 67 causes of delay under 9 major

groups such as Project team, Owner, Contractor, Consultant,

Architect, material, labour, equipment and external factors.

Then a ranking method is done based on relative importance

index method to find major cause of delay. It is found that the

most common factors of delay which is repeated in most of the

project are lack of funds to finance the project to completion,

labour shortage, material shortage, lack of effective

communication, lack of supervision and changes in drawings.

The outcome of the project is to provide recommendation to

control delay in the project during construction phase.

Keywords— Delay analysis technique, causes of delay, tools

to evaluate delay in construction, delay control measure

INTRODUCTION

In construction, delay could be defined as the time overrun

either beyond completion date specified in a contract or

beyond the date that the parties agreed upon for delivery of a

project. It is a project slipping over its planned schedule. The

delay in the project has an adverse effect on project success

in terms of time, cost and quality. The objective of the project

is
• To identify delay factors in construction projects

• To rank the delay factors according to the importance
level on delays in project

•To find the tools to analysis and evaluate the time delay
factors in the construction building.

•Recommendations to control delay during construction
phase for construction project

I. STUDY ON DELAY ANALYSIS

A. Construction project planning

Planning explains “what” is going to be done, “how”,

“where”, by “whom”, and “when” for effective monitoring

and control of complex projects. The objective of project

planning is to complete the construction within the specified

time and budget. In construction project planning the steps

need to be identified are as follows.

•Feasibility of the project

•Project management plan

•Identifying the constraints in the project (time, cost,

resources)

•Project delivery method, stakeholders, funding sources

•Construction method

•Identifying risk in project

•Milestone, duration and budget

•Roles and responsibility

•Preparation of contract documentation

B. Project scheduling

Project scheduling covers only the issue of when? i.e. when

works need to be done and completed. By doing project

scheduling it helps to control and measure the project

duration and provides information for timely decisions to be

taken when there is a change in schedule. The results of doing

a detailed project schedule are duration of the project and

completion date can be easily tracked, helps to calculates the

start or end of a specific activity, evaluate the effect of

changes, improves work efficiency, predict and calculate the

cash flow, resolve delay claims and it serves as an effective

project control tool

C. Types of project scheduling

Selection of the most appropriate scheduling technique

depends on the size and complexity of the construction

Project, the preferences of the entity preparing the schedule,

and the scheduling requirements of the Contract. The most

common scheduling techniques used for construction projects

are Gantt Charts or bar charts, linear schedules, program

evaluation and review technique and Critical Path Method

(CPM) schedules.

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D. Progress monitoring

When updating a project, actual progress is recorded for

each activity relative to the date of each update. This regular

update will include progress on values for: dates on which

activities started or finished actual percent of work completed

within each task, actual resources expended on each task and

actual cost expended on each task. There are six basic

techniques for measuring the progress of a task in a CPM

network as follows: Unit Measure, Incremental Milestones,

Start/finish, Observational Assessment, Level of Effort/Cost

Ratio and Equivalent Units

E. Classification of construction delays

The classification of delays is dependent upon the type

and magnitude of the effect that an activity will have on the

project and who is responsible for the delay among the stake

holders. Hence they are classified into four categories such as

Critical or noncritical, Excusable or non-excusable,

Compensable or Non-compensable and Concurrent or Non-

concurrent.

Critical Versus Non-Critical Delays

The delays that affect the project completion time or date are

considered as critical delays. And the delays that do not affect

the project completion time or date are noncritical delays. If

certain activities are delayed in the construction project life

cycle, the project completion date will be delayed. The

determining which activities truly control the project

completion date depends on the following: The project itself,

the contractor„s plan and schedule (particularly the critical

path), the requirement of the contract for sequence and

phasing and the physical constraint of the project.

Excusable and Non-Excusable Delays

Delay that is due to an unforeseeable event beyond the

contractor„s or the subcontractor„s control. Normally, based

on common general provisions in public agency

specifications, delays resulting from the following events

would be considered excusable: General labor strikes, fires,

floods, act of God, owner-directed changes, errors and

omissions in the plans and specifications, differing site

conditions or concealed conditions, unusually severe weather

Non-excusable delays are events that are within the

contractor„s control or that are foreseeable. These are some

examples or non-excusable delays: Late performance of sub-

contractors, untimely performance by suppliers, faulty

workmanship by the contractor or subcontractors, a

project-specific labor strike caused by either the

contractor„s unwillingness to meet with labor

representative or by unfair labor practice

Compensable and Non-Compensable Delays

Compensable delay is caused by the owner or the owner’s

agents. A compensable delay is a delay where the contractor

is entitled to a time extension and to additional compensation

such as payment for the delay.

Non-compensable delay is caused by third parties or incidents

beyond the control of both the owner and the contractor

where the contractor is normally entitled to a time extension

but no compensation for delay damages

Concurrent or Non-concurrent.

Concurrent delays are two or more parallel and independent

delays to the critical path of a project. Concurrent delays can

be on the same critical path or on a parallel critical path

F. Delay Analysis Techniques

Delay analysis is a analytical process that should be

employed with project documentation along with collected

data from project site. The selection of delay analysis

depends on the variety of factors and the available records.

There are five commonly used delay techniques.

1. Impacted as-planned method

2. Time impact analysis method

3. Collapsed as-built or but-for analysis method

4. Windows analysis method

5. As-planned versus as-built (Total time) method

Impacted as-planned method

According to Trauner et al. (2009), in this method the analyst

specifies the as planned schedule, and inserts into this

schedule the changes which caused project delays. These

changes are the only determined delays recorded during

construction process which may have affected the project

duration. Trauner et al. (2009) point out the major

weaknesses of this method as it does not reflect the dynamic

nature of construction project and the critical path.

Time impact analysis method

The analyst determines the amount of project delay

resulted from each of the delaying activity successively by

calculating the difference between the project completion

date of the schedule after the addition of each delay and

that prior to the addition (Ndekugri, Braimah, and

Gameson, 2008).

Collapsed as-built or ‗ ‘but-for’ analysis method

In this method, the analyst studies all contemporaneous

project documentation and prepares a detailed as-built

schedule instead of an as-planned schedule as mentioned in

the what-if method. The analyst subtracts or removes

activities which affected the project from the as-built

schedule (Trauner et al. 2009).

Windows analysis method

Window analysis method is also called the contemporaneous

period analysis and snapshot method. In this method, the

basic concept is that the total project duration of CPM

schedule is divided into digestible time periods or windows

(e.g., monthly) and the delays that occurred in each windows

of time are analyzed successively by focusing on the critical

paths (Hegazy and Zhang, 2005).

As-planned versus as-built (Total time) method

Basically, the main concept is that the as-planned versus

as-built method compares two schedules, which is why it is

also called “the total time method or net impact method”.

In this method the assumption is that one party (contractor)

causes no delays and other party (owner) causes all

delays.

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G. Programme updates

It is used to document the performance of the employer,

the professional team, designers, and the contractor and their

ability to meet commitment dates. Programmes are updated

to communicate actual project status from time to time, keep

the programme relevant as a useful management tool, record

actual performance of all parties‟ alike, record changes to the

original plan and support forensic or prospective delay

analysis. When no frequency is specified, it is unlikely that a

contractor will submit updated CPMs to the employer until

extensions of time are granted or significant changes to scope

or sequence are incorporated into the project. The minimum

data required to properly update a programme would be

percentage complete, remaining duration (%), actual start,

and actual finish.

H. Records

Once the program update is done then changes need to be

recorded. When good record keeping procedures are

established and maintained, contract administrators are often

able to access key information quickly and in a timely enough

manner to respond to crises and manage problems at the time

they arise. Many standard forms require contractors to

provide notice of an intention to make a claim for time and/or

money within a reasonable time after the event which gave

rise to the claim. Records can be inspected by the employer‟s

representative from time to time. For each delay event an

„event analysis‟ needs to be done.

II. QUESTIONNAIRE SURVEY

The Survey is designed based on the objective of the study
to find out the causes of delays in construction projects

and effect of the delays on overall project. The Survey

is framed in such a way that the personal view of

different people involved in different projects (Architect,

Consultant, Owner, Project manager, Contractor) is

collected and analyzed. This questionnaire consists of 63

causes of delay on which a detailed analysis will be carried

out by using statistical concept. These causes are classified

into nine groups according to the sources of delay: Factors

related to Project, Owner, Contractor, Consultant,

Architect/design-team, materials, equipment, manpower

(labor), and external factors.

A. Questionnaire format

Respondents are asked to fill What is the frequency of

occurrence for this cause?. The frequency of occurrence was

categorized as follows: always, often, sometimes and rarely

(on 4 to 1 point scale). Respondents are required to fill the

respective places with only scale points (1, 2, 3 and 4) of their

opinion.

Frequency of Occurrence

Always (4): Generally occurs in all the projects (70%-100%).

Often (3): Occurs in 5 to 7 projects out of 10 projects (50%-

70%).

Sometimes (2): Occurs in 1 to 5 projects out of 10 projects

(10%-50%).

Rarely (1): Occurs only 1 time out of 10 projects (>10%).

The questionnaire format is provided in appendix

B. Respondent’s profile

The questionnaires were distributed to Owners, Project

Manager, Architect, Consultants and Contractors of Indian

construction industry. The respondents involved in the

survey had several years of experience in handling various

types of projects. The characteristics of the respondents

participated in survey are summarized below. Population

sample of 35 was used in this survey. A total sample of 31

was deployed.

Fig. 1. Result of respodents

Fig. 2. Working experience

III. QUESTIONNARIE SURVEY RESULTS

The collected responses from different categories of people

involved in construction project gives the major causes of

delay factor faced in the construction process. The mean of

each group of question is calculated using Relative

Importance Index to calculate the ranking and the percentage

of delay cause in the building. The final result showing the

contribution of different factors on the delay of a construction

project is shown below

0
2

4
6

8
10

Result of respondents

0

10

20

30

40

50

less than 10

years

11-15 years 16-20years 20 years and

above

working experience

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Vol. 4 Issue 03, March-2015

1078

TABLE I. RANKING FOR DELAY CAUSES

No Cause Of Delay Points Rank % Group

1 Very short original contract duration 20 17

Project

team

2 Legal disputes between parties 55 46

3

Inadequate definition of substantial

completion 50 42

4 Ineffective delay penalties 35 29

5 Types of construction contract 40 33

6 Types of project bidding 55 46

7 Payment delay 70 58

Owner

8 Delay in delivering the site 57 48

9 Change order 80 67

10 Late approval of design document 51 43

11 Late approval of sample material 54 45

12 Lack of communication 82 68

13 Late decision making 40 33

14 Conflicts between partners 30 25

15

Unavailability of incentives for contractor

for finishing ahead of schedule 45 38

16 Suspension of work 20 17

17 Financing difficulty 72 60

Contractor

18 Conflicts with sub-contractor 50 42

19 Rework 70 58

20 Poor site management and supervision 60 50

21

Poor coordination with labor and

subcontractor 65 54

22 Ineffective planning and scheduling 60 50

23 Improper construction method 40 33

24 Delay in sub-contractor work 45 38

25 Lack of knowledge 50 42

26 Frequent change of subcontractor 45 38

27 Poor qualification of technical staff 52 43

28 Site mobilization delay 52 43

29 Inspection and testing delays 52 43

Consultant

30 Approval delay 45 38

31 Poor communication 62 52

32 Conflict between consultant & architect 45 38

33 Lack of experience 45 38

34 Errors in design document 50 42

Architect

35 Delay in producing design documents 65 54

36 Inadequate details in drawing 51 43

37 Insufficient data collection & survey 45 38

38 Misunderstanding of owners requirement 45 38

39 Unused advanced design software 52 43

40 Shortage of material 70 58

Materials

41 Change in specification 60 50

42 Late delivery 65 54

43 Damaged of required material 45 38

44 Delay in manufacturing 54 45

45 Late procurement 60 50

46 Lack of material availability 54 45

47 Shortage of equipment 61 51

Equipment

48 Equipment break down 62 52

49 Poor operator skill 50 42

50 Low productivity & efficiency 52 43

51 Lack of high technology equipment 65 54

52 Shortage of labor 71 59

Labor

53 Personal conflicts 50 42

54 Lack of knowledge 60 50

55 Lack of communication 72 60

56 Lack of skilled labor 80 67

57 Poor soil condition 45 38

External

Factors

58 Delay in obtaining permits 76 63

59 Climatic factor 75 63

60 Unavailability of utilities 44 37

61 Accidents during construction 42 35

62 Changes in government regulation 65 54

63 Delay in final inspection 60 50

A. Highest percentage of delay group

From the above finding and analysis using ranking

method the group which is more responsible for the delay in

the project is find out. According to the survey result it is

found that resources are the main reason for the delay in the

project along with external factors it is then followed by

Contractor, then Owner and the others.

Fig. 3. Highest percentage of delay group

0 20 40 60 80

Project Group

Owner

Contractor

Consultant

Architect

Material

Equipment

Labor

External Factors

Points

International Journal of Engineering Research & Technology (IJERT)

ISSN: 2278-0181

www.ijert.orgIJERTV4IS031166

(This work is licensed under a Creative Commons Attribution 4.0 International License.)

Vol. 4 Issue 03, March-2015

1079

B. Template to evaluate time delay
The tools to evaluate and analysis time delay factors are CPM

and PERT. The collected data from the tools should be filled

in template for event analysis.

TABLE II. EVENT ANALYSIS SHEET

DESCRIPTION FORMULA VALUE

Planned quantity PQ

Planned duration PD

Planned productivity PP

Total budget TB

Cost per unit C TB/PQ

Actual quantity AQ

Actual duration AD

Actual productivity AP

Planned value PV, BCWS (AD*TB)/PD

Actual cost AC, ACWP C*AQ

Earned Value (EV) BCWP
EV = PV x(

AP/PP)

Cost Variance CV
EV-AC
(BCWP -ACWP)

Cost Variance % CV% CV/EV

Cost Performance

Indicator
CPI EV/AC

To Complete Cost

Performance Indicator
TCPI

(TB-EV)/(TB-

AC)

Schedule Variance SV
EV-PV

(BCWP- BCWS)

Schedule Variance % SV%
SV/PV

(SV/BCWS)

Schedule Performance

Indicator
SPI EV/PV

To Complete Schedule

Performance Indicator
TSPI

(TB-EV) / (TB –

PV)

Budget At Completion BAC = TB

Estimate At Completion EAC AC +(BAC- EV)

Variance At Completion VAC BAC – EAC

Planned % Completed PV / BAC

% Completed Actual AC / EAC

C. Recommendations

From the survey it is found that contractor has the highest

percentage of cause of delay followed by owner and then

consultant. So recommendation to control major causes of

delay are listed below

TABLE III. RECOMMENDATIONS FOR MAJOR CAUSES OF DELAY CAUSES

Causes of delay Recommendations

Weather

condition

Conducting detailed and perfect surveys towards

the field condition and previous weather data

External factors Monitor the work done by the earlier contractors to
make sure that delays outside your control are

recognized and documented.

Lack of funds Optimize cash flow in accordance with the

requirements and make sure fund needed for
project is available to execute the project

Deviation of

scheduling

Develop detailed and accurate schedule to

facilitate easy and controlled scheduled execution

Lack of
communication

Planning and applying Management Information
System(MIS)

Poor decision

making process

Conduct routine/regular coordination meeting and

develop a procedure regarding decision making.

Lack of

coordination /

Wrong
delegation of

authority

Develop a good, simple and easy to understand

system to regulate coordination procedures and

responsibility of units. Make organization chart
with detail job description which includes

responsibilities and roles of each function

Lack of

inspection

Provide separate technical staff or site manager for

periodic inspection and monitoring work process
which includes starting late, late submission of

drawings, mistakes or errors, resource availability,

etc. then proper record has to be maintained to
detect risk and mitigate.

Improper

planning

Understand the level of supply and demand to

produce detail planning and schedule.

Implement automatic machine work to avoid

shortage of labor such as automatic plastering

machine, wall painting, precast concrete wall, etc.

Lack of

knowledge

Contractor needs to aware of new technology and

techniques to reduce time duration for activity or

labor force

Lack of facilities

at site

Site management should be properly done to

ensure proper resource; basic facilities for worker

are available to increase productivity by doing

detail study in site condition.

Poor selection of

vendors

Consider supplier daily capacity and material

quality for selecting vendors to avoid delay and

conflicts.

Labor shortage Early workforce planning is essential for owners

and contractors to effectively manage project labor

risks. Then providing incentives/awards for

workers like best employer of the year/ month so

that productivity and quality of work will be

increased.

Skilled labor

shortage

Providing training and upgrade skills to use new

technology and techniques for unskilled labors to

increase productivity and efficiency of the worker.

International Journal of Engineering Research & Technology (IJERT)

ISSN: 2278-0181

www.ijert.orgIJERTV4IS031166

(This work is licensed under a Creative Commons Attribution 4.0 International License.)

Vol. 4 Issue 03, March-2015

1080

D. Conclusion

The major causes of delay which is found repeating in

almost every project are external factors, financial

difficulties, shortage of labor, insufficient labor productivity,

owner interference and improper planning. After analyzing

the data it is clear that the contribution of Contractor in

delay of the construction project is high then followed by

client then consultant side and others. Resource allocation is

the main criteria for doing schedule planning to allocate

duration for each activity included in the project so that delay

in the construction project can be reduced.

ACKNOWLEDGMENT (Heading 5)

I extend my gratitude to our Faculty Head Dr. A. Lilly
Rose, M. Arch., PhD, Head of the Department Dr. N.
Jothilakshmy, B. Arch; M.T.P., PhD, Assoc. Prof.T.Vennila
M.Arch, Mr.S.Kavin Kumar and Assoc. Prof. Ar. K. Suresh
Babu for their helpful suggestions and comments during my
project presentation. Mr.K.Gopala Krishnan, Mr.Karthik
Mohan, Mr.G.Hemanth kumar and my parents for their help
and support to complete the project.

REFERENCES

[1] Aditi Dinakar “Delay Analysis in Construction Project”, IJETAE, Vol.
4, No. 5, May 2014

[2] Aftab Hameed Memon, “Contractor Perspective On Time Overrun
Factors In Malaysian Construction Projects”, IJSET, Vol. 3, No. 3,
2014

[3] Ashwini Arun Salunkhe & Rahul S. Patil, “Effect of Construction
Delays on Project Time Overrun: Indian Scenario”, IJRET, eISSN:
2319-1163 | pISSN: 2321-7308

[4] “Construction Delay Analysis Methods”,
http://www.forensisgroup.com/expert-articles/construction-delay-
analysis-methods, 2013

[5] Roger Gibson “Construction delays: Extension of time and
prolongation claims”

[6] Desai Megha & Dr Bhatt Rajiv, “A Methodology For Ranking of
Causes of Delay For Residential Construction Projects In Indian
Context “, IJETAE, Vol. 3, No. 3, March 2013

[7] Enas Fathi Taher & R.K. Pandey, “Study of Delay in Project Planning
and Design Stage of Civil Engineering Projects”, IJEAT, Vol. 2, No.3,
February 2013

[8] Owolabi James D & *Amusan Lekan M. Oloke C., “Causes And Effect
of Delay on Project Construction Delivery Time” IJER, Vol. 2 No. 4
April 2014

[9] P. J. Keane & A. F. Caletka, “Delay Analysis in Construction
Contracts”, A John Wiley & Sons, Ltd., Publication 2008, United
Kingdom

[10] Songül Dayi “Schedule Delay Analysis In Construction Projects: A
Case Study Using Time Impact Analysis Method”, The Graduate
School Of Natural And Applied Sciences of middle East Technical
University, December 2010

[11] Theodore J. Trauner Jr., “Construction Delays: Understanding Them
Clearly, Analyzing Them Correctly”, 2009

APPENDIX

Name Date

Designation Location

Work Experience

Email Id

No Cause of delay

Alway

s Often

Some

times Rarely Group

1

Original contract
duration is too

short

Project

team

2
Legal disputes
between parties

3

Inadequate

definition of
substantial

completion

4

Ineffective delay

penalties

5

Types of

construction
contract

6

Type of project

bidding

7

Delay in progress

payment by owner

Owner

8

Delay to furnish
and deliver the

site to the

contractor by
owner

9

Change order

during

construction

1

0

Late in approval

design document

by owner

1

1

Delay in

approving shop
drawings and

sample material

1

2

Lack of

communication
between owner

and contractor

1
3

Slowness in

decision making
process

1
4

Conflicts between

joint ownership of
the project

1

5

Unavailability of

incentives for
contractor for

finishing ahead of

schedule

1
6

Suspension of
work by owner

1
7

Difficulties in

financing project
by contractor

Contra

ctor
1

8

Conflicts in

subcontractor

schedule in
execution of the

projec

Statistics homework help

MATH 215 Assignment 2.docx


MATH 215 Assignment 2

Khadra Sulub

Victor Olobatuyi

March, 30th/ 2022

Assignment 2

Overview

Total marks:   / 71

This assignment covers content from Unit 2 of the course. It assesses your knowledge of the concepts and rules that allow us to compute the probabilities related to events that occur when conditions are uncertain.

Instructions

Show all your work and justify all of your answers and conclusions, except for the True/False questions.

Keep your work to 4 decimals, unless otherwise stated.

(4 marks)

Circle True (T) or False (F) for each of the following statements:

T F {H, T} represents the sample space for an experiment of flipping two coins, each with heads (H) on one side and tails (T) on the other.

T F 13/12 represents a possible value of a probability.

T F Suppose that the probability of event A occurring is 1/5 and the probability of event B occurring is 3/7. If events A and B are mutually exclusive, the probability that A and B occur together is 0.

T F If a researcher samples without replacement, then future probabilities of the sampling process are unaffected by prior probabilities.

(7 total marks)

At a recent convention, a group of 60 doctors were classified according to their specialties. The number of doctors in each specialty was summarized as follows:

Pediatrician: 18 General Practitioner: 29 Surgeon: 4 Dermatologist: 9
If a doctor is selected at random, what is the probability that:

(1 mark)

the doctor is a dermatologist?

The probability is 0.15

(2 marks)

the doctor is either a pediatrician or a general practitioner?

The probability 0.84

(2 marks)

the doctor is not a pediatrician?

The probability is 0.3

(2 marks)

the doctor is neither a general practitioner nor a dermatologist?

The probability is 0.36

(19 marks)

An analysis of blood donors examined blood type (A, B, AB or O) and whether the donor was male or female. The data is represented in the following table:

Gender

A

B

AB

O

Male

 (M)

35

16

2

40

Female

 (F)

29

25

5

38

In the questions below, round all calculated probabilities to 4 decimal places.

(3 marks)

1. What is the probability that a randomly selected donor is female?

The probability 0.4

(4 marks)

1. What is the probability that a randomly selected donor is either male or has type O blood?

The probability is 0.43

(4 marks)

1. What is the probability that a randomly selected donor is neither female nor has type AB blood?

The probability is 0.97

(2 marks)

1. What is the probability that a selected donor has type AB blood, given that he is male?

The probability is 0.02

(2 marks)

1. Are the events that a person has type A blood (denoted by A) and that a person is female (denoted by F) mutually exclusive? Explain.

The two events are independent if the probability P(AՌB) of their intersection AՌBis equal to the product P(A)-P(B) of their individual probabilities

(4 marks)

1. Are the events that a person has type B blood (denoted by B) and that a person is female (denoted by F) independent? Justify your conclusion using the appropriate rule(s) of probability.

The two events are independent if the equation P (AՌB) = P (A). P(B)holds true you can use the equation to check if events are independent,

(13 total marks)

Three patients are accepted into a clinical trial for a new drug. According to the severity of the condition of each patient, the doctors estimate that the probability that the drug will be effective for Patient A is 0.7, the probability that it will be effective for Patient B is 0.2, and the probability that it will be effective for Patient C is 0.6. Assume that the success of the drug for the three patients is independent.

(8 marks)

1. Draw a tree diagram displaying all outcomes and joint probabilities measuring the effectiveness of the drug for all three patients.

A

AB

0.7 A

AB

0.2 B

BC

0.6 C CA

C

(1 mark)

1. What is the probability that the drug will be effective for Patient B only?

The Probability is 0.2

(1 mark)

1. What is the probability that the drug will be effective for at least one of the patients?

The probability is 0.5

(3 marks)

1. What is the probability that the drug will be effective for exactly two of the three patients?

The probability is 1

(11 total marks)

The Math Club is picking names out of a hat to determine who will serve as the Executive for their group. The person whose name is drawn first will serve as the President, and the person whose name is drawn second will be Vice-President. The Math Club has 13 members: 5 members whose focus of study is Statistics and 8 members whose focus of study is Calculus. [
Hint:
A tree diagram would be helpful in analyzing this problem.]

What is the probability that:

(2 marks)

1. Both members chosen for the executive have Calculus as their focus of study?

The probability is 0.8

(5 marks)

1. Any one member of the Executive has Statistics as a focus, and the other has Calculus as a focus?

The probability is 0.15

(2 marks)

1. The chosen President has Calculus as a focus and the chosen Vice-President has Statistics as a focus?

The probability is 0.152

(2 marks)

1. At least one member of the chosen Executive has a focus in Calculus?

The probability is 0.08

(6 total marks)

A survey questioned 200 individuals regarding their intention to vote (Conservative, Liberal or Other) in an upcoming election. It was found that 50% of the sample planned to vote Conservative and 40% planned to vote Liberal. Fifty percent of the men indicated that they planned to vote Liberal, and forty percent of the men planned to vote Conservative. Overall, 30% of the sample were women.

(5 marks)

1. Construct a two-way classification for these survey results.

Conservative

Liberal

Total

Men

80

60

140

Women

35

25

60

Total

115

85

200

(1 mark)

1. Circle True (T) or False (F) for the following statement:

T F In this example, male and female are complementary events.

(11 total marks)

You are given the probabilities of events A, B and C as listed below:

(2 marks)

1.

Find .

P( A and C)

= 0.14

(2 marks)

1.

Find .

= 1.14

(2 marks)

1.

Find .

= P(BՌC)/P(C)

= 0.571

(2 marks)

1. Are B and C mutually exclusive events? Why?

B and C have no members in common, you cannot have all tails and heads at a time

(3 marks)

1. Are B and C independent events? Provide a mathematical justification of your conclusion using the appropriate rule(s) of probability.

B and C are independent events for example P(A and B and C)= P(A)*P(B)*P(C)


MATH 215 Assignment 3.docx



MATH 215 Assignment 3

Khadra Sulub

Victor Olobatuyi

April, 5th/ 2022

Assignment 3

Overview

Total marks:   / 75

This assignment covers content from Unit 3 of the course. It assesses your knowledge of random variables, types of random variables and various types of probability distributions, along with their means and standard deviations.

Instructions

Show all your work and justify all of your answers and conclusions, except for the True/False questions.

Keep your work to 4 decimals, unless otherwise stated.

(4 marks)

Circle True (T) or False (F) for each of the following statements:

T F The following table, which lists values of x and their probabilities, represents a valid probability distribution:

x

P(x)

3

0.32

4

0.54

5

0.24

T F The following table, which lists values of x and their probabilities, represents a valid probability distribution:

x

P(x)

0

.09

1

0.28

2

0.42

3

0.39

T F The speed of a car travelling on the Queen Elizabeth Highway is an example of a continuous variable.

T F The binomial distribution can be used only when the probabilities of the two possible outcomes are equal.

(16 marks)

The following table lists the frequency distribution of the number of vehicles owned per household from a sample of 200 households:

x

 0

  1

 2

 3

4

5

f

33

106

45

10

4

2

(4 marks)

Construct a probability distribution table for the number of vehicles owned per household.

X

F

P(x)

0

33

0.33

1

106

1.06

2

45

0.45

3

10

0.10

4

4

0.4

5

2

0.2

(2 marks)

Calculate the mean of this probability distribution. Hint: Consider adding the appropriate column to the table created in part (a).

=Sum/count

200/6

=33.33

(4 marks)

Calculate the standard deviation of this probability distribution. Hint: Consider adding the appropriate columns to the table created in part (a).

SD=19.9

(4 marks)

Give a brief interpretation (one or two sentences each) of the values of the mean and the standard deviation.

Use the mean to describe the sample with the single value that represents the center of the data

The standard deviation is the average amount of variability in your date sheet

(2 marks)

What is the probability that a household selected at random will have at least two vehicles?

The probability is 0.2

(13 total marks)

When transferring a goldfish to a new water source, such as a different fish tank, there is an 8% chance that the goldfish will die within the first week.

If we select at random 5 goldfish that have been transferred to a new water source, what is the probability:

(3 marks)

1. that exactly one of them will die within the first week?

Ans: 0.4

(6 marks)

1. that fewer than three of them will die within the first week?

Ans: 1.2

(2 marks)

1. that at least one of them will die within the first week?

0.4

(2 marks)

1. Circle True (T) or False (F) for each of the following statements:

T F If we randomly select 6 goldfish that have been transferred instead of 5, the experiment continues to satisfy the conditions for a binomial experiment.

T F John transfers each goldfish to the same bowl. In this case, the chance that a goldfish will die goes up by 1% for each additional goldfish that is selected. This new experiment continues to satisfy the conditions for a binomial experiment.

(11 total marks)

Thirty percent of students graduate from high school before they reach the age of 18. In a random sample of 16 high-school graduates, what is the probability that:

[
Hint:
Use binomial table.]

(3 marks)

1. more than 10 of them graduated before they were 18 years old?

No,

(3 marks)

1. at most 4 of them graduated before they were 18?

Yes

(3 marks)

1. fewer than 7 of them graduated after they turned 18?

Yes

(2 marks)

1. Would the binomial probability distribution representing the sample in Question 4a be skewed? If yes, in what direction? Describe the shape of the distribution in context of the study.

The binomial distribution formula is for random variable X, given by; P(x:n,p)

P is Probability of success in a single experiments

(5 total marks)

Use the standard normal distribution table to find:

(2 marks)

1.

z

+0.00

+0.01

+0.02

+0.03

+0.04

+0.05

+0.06

+0.07

+0.08

1.1

0.5623

0.5625

0.5627

0.5631

0.5632

0.5635

0.5645

0.5646

0.5649

1.2

0.5723

0.5734

0.5635

0.5635

0.5635

0.5635

0.5635

0.5635

0.5663

1.3

0.5635

0.5635

0.5635

0.5635

0.5635

0.5635

0.5635

0.5635

0.5765

1.4

0.5635

0.5635

0.5635

0.5635

0.5635

0.5635

0.5635

0.5635

0.5735

1.5

0.5635

0.5635

0.5635

0.5635

0.5635

0.5635

0.5635

0.5635

0.5635

1.6

0.5635

0.5635

0.5635

0.5635

0.5635

0.5635

0.5635

0.5635

0.5635

1.7

0.5635

0.5635

0.5635

0.5635

0.5635

0.5635

0.5635

0.5635

0.5635

(3 marks)

1.

z

+0.10

+0.20

+0.30

+0.40

+0.50

+0.60

+0.70

+0.80

+0.90

2.0

0.5623

0.5625

0.5627

0.5631

0.5632

0.5635

0.5645

0.5646

0.5649

2.01

0.5723

0.5734

0.5635

0.5635

0.5635

0.5635

0.5635

0.5635

0.5663

2.02

0.5635

0.5635

0.5635

0.5635

0.5635

0.5635

0.5635

0.5635

0.5765

2.03

0.5635

0.5635

0.5635

0.5635

0.5635

0.5635

0.5635

0.5635

0.5735

2.04

0.5635

0.5635

0.5635

0.5635

0.5635

0.5635

0.5635

0.5635

0.5635

2.05

0.5635

0.5635

0.5635

0.5635

0.5635

0.5635

0.5635

0.5635

0.5635

2.06

0.5635

0.5635

0.5635

0.5635

0.5635

0.5635

0.5635

0.5635

0.5635

(11 total marks)

The daily milk production of a dairy cow is normally distributed with a mean of 3,500 milliliters and a standard deviation of 250 milliliters.

(4 marks)

1. What is the probability that a cow selected at random will produce between 3,200 and 3,855 milliliters of milk per day?

The Probability is 0.3

(4 marks)

1. What is the probability that a cow selected at random will produce 3,900 milliliters of milk or more?

The probability is 0.34

(3 marks)

1. Forty percent (40%) of cows will likely produce less than what amount of milk, in milliletres?

Yes

(4 marks)

The time taken to assemble a car in a certain plant is a normal random variable having a mean of 20 hours. If 6.3% of the cars assembled take longer than 25 hours to assemble, what is the standard deviation of assembly time?

SD= 3.96

(11 total marks)

A national poll found that 60% of Canadians believe that life exists on other planets. In a randomly selected sample of 300 Canadians:

(3 marks)

1. what is the probability that fewer than 200 people in the sample believe in extraterrestrial life?

The probability is 0.2

(4 marks)

1. what is the probability that at least 160 people in the sample believe in extraterrestrial life?

The probability is 0.16

(4 marks)

1. what is the probability that exactly 190 Canadians in the sample believe in extraterrestrial life?

The probability is 0.19

1.

These extra pages are for additional calculations. If you need them for your solutions, please reference them in the appropriate place in the questions.


MATH 215 Assignment 4.docx



MATH 215 Assignment 4

Khadra Sulub

Victor Olobatuyi

April, 13th/ 2022

Assignment 4

Overview

Total marks:   / 92

This assignment covers content from Unit 4 of the course. It assesses your knowledge of sampling distributions that refer to probability distributions of sample statistics, such as the sample mean and sample proportion, and your ability to use sampling distributions in estimation and in hypothesis testing about population means and population proportions.

Instructions

Show all your work and justify all of your answers and conclusions, except for the True/False questions.

Keep your work to 4 decimals, unless otherwise stated.


Note:
Finishing a test of hypotheses with a statement like “reject ” or “do not reject ” will be insufficient for full marks. You must also provide a written concluding statement in the context of the problem itself. For example, if you are testing hypotheses about the effectiveness of a medical treatment, you must conclude with a statement like, “we can conclude that the treatment is effective” or “we cannot conclude that the treatment is effective.”

(9 total marks)

The duration of long-distance telephone calls is normally distributed with a mean of and a standard deviation of . If a random sample of 64 telephone calls is used to reflect on the population of all long-distance calls, what is the probability that the sample mean call duration:

(3 marks)

will be more than 14 minutes?

Yes

(6 marks)

will be either less than 15 minutes or more than 20.5 minutes?

Its more than 20.5%

(7 total marks)

An insurance company states that 8% of all house insurance claims are fraudulent. If this estimate is correct, what is the probability that in a random sample of 184 house insurance claims, the proportion of claims that are fraudulent is

(3 marks)

1. less than 0.05?

Its true

(4 marks)

1. more than 0.10?

No

(11 total marks)

Researchers were interested in the number of monitors and screens (televisions and computer monitors) owned within households in Canada. They collected data from a random sample of ten households. The number of monitors/screens for the ten households was as follows:

5 8 1 3 3 4 2 7 6 4
(8 marks)

1. Assuming that this variable is normally distributed, construct a 90% confidence interval for the population mean.

Ans: 39.4

(2 marks)

1. In a sentence or two, describe what this confidence interval represents.

Ans: The probability that a parameter will fall between a pair of values around the mean. Confidence intervals measures the degree of uncertainty or certainty in a sampling method

(1 mark)

1. Which of the following would produce a confidence interval with a larger margin of error than the 90% confidence interval? Clearly circle only one response.

Sampling only 5 households instead of 10, because 5 are easier to manage.

Sampling 5 households rather than 10, because a smaller sample size will result in a larger margin of error.

Sampling 20 households rather than 10, because a larger sample size will result in a larger margin of error.

Computing an 85% confidence interval rather than a 90% confidence interval, because a larger confidence interval will result in a larger margin of error.

(10 total marks)

The manager of a large production plant would like to estimate the mean amount of time a worker takes to assemble a new component. A random sample of 64 workers indicates a mean time of 16.2 minutes. Assume that the population standard deviation of this assembly time is known to be 3.6 minutes.

(5 marks)

1. Construct a 95% confidence interval for the mean assembly time.

(4 marks)

1. How many workers should be involved in this study in order to have the mean assembly time estimated within 0.5 minutes of the population mean with 97.5% confidence?

(1 mark)

1.

Which of the following is a property of the sampling distribution of the sample mean, ? Clearly circle one response only.

1.

If you increase your sample size, the sample mean, , will always get closer to the population mean, .

1.

The standard deviation of the sample mean is generally larger than the standard deviation from the original population,

1.

The mean of the sampling distribution of is ,the population mean.

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(8 total marks)

A researcher was interested in the enrollment of women within engineering majors at a local university. The data from a random sample of 25 engineering students were as follows:

Male Female Male Male Male Female Male Male Male Male Male Female
Female Male Male Male Male Male Male Female Male Female Male Male Male

(7 marks)

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(1 mark)

1. Suppose that we took a second sample and calculated that this sample had a 90% confidence interval of 0.19 to 0.35. Which of these is a valid interpretation of this confidence interval? Clearly circle only one response.

1. There is a 90% probability that a randomly selected student has a 0.19 to 0.35 probability of being female.

1. We are 90% confident that the mean proportion of being female in our sample is between 0.19 and 0.35.

1. We are 90% confident that 19 to 35% of female students will chose an engineering major.

1. We are 90% confident that the population mean proportion of females is between 0.19 and 0.35.

(8 total marks)

Suppose a consumer advocacy group would like to conduct a survey to find the proportion of consumers who bought the newest model of a particular vehicle who were happ

Statistics homework help

Clinical Practice in Pediatric Psychology
Early Weight Loss in Adolescent Weight Management: The Role of the
Home Environment
Katherine E. Darling, Manfred H. M. van Dulmen, Geoffrey E. Putt, and Amy F. Sato
Online First Publication, February 3, 2022. http://dx.doi.org/10.1037/cpp0000434

CITATION
Darling, K. E., van Dulmen, M. H. M., Putt, G. E., & Sato, A. F. (2022, February 3). Early Weight Loss in Adolescent Weight
Management: The Role of the Home Environment. Clinical Practice in Pediatric Psychology. Advance online publication.
http://dx.doi.org/10.1037/cpp0000434

Early Weight Loss in Adolescent Weight Management: The Role of
the Home Environment

Katherine E. Darling1, Manfred H. M. van Dulmen1, Geoffrey E. Putt2,
and Amy F. Sato1

1 Department of Psychological Sciences, Kent State University
2 Pediatric Psychiatry and Psychology, Akron Children’s Hospital, Akron, Ohio, United States

Objective: Successful weight loss early in treatment is a key factor for long-term weight
management success in adolescence. Yet prior research has not examined factors in the
home environment related to risk for increased weight status as potential predictors of
early weight management success. The primary goal of the present study was to
explore the impact of modifiable household factors on baseline weight status and early
weight status change among adolescents participating in an outpatient weight
management program to identify clinical targets of early intervention. Method: Parents
of adolescents (N = 188) presenting to an interdisciplinary weight management clinic
within a children’s hospital completed measures at initial presentation. Objective
adolescent weight status was collected at baseline and 2-month follow-up (n = 97).
Results: Household chaos was significantly associated with weight status at
presentation to the clinic, F(3, 181) = 3.85, p = .011. Similarly, household chaos was
the only unique predictor of weight change from baseline to 2 months, F(3, 92) = 3.03
p = .033. Conclusions: Household factors, particularly household chaos, have often
been overlooked in the adolescent obesity literature but are likely key contributors to
early intervention response in a clinical weight management. This study highlights the
importance of assessing and intervening on chaos in the household as higher levels of
chaos may negatively impact early treatment outcomes among adolescents with obesity.

Implications for Impact Statement
The present study suggests that household chaos may be a key modifiable factor
impeding adolescent weight loss early in treatment. Although not often considered
in prior research, chaos may serve as a key target for future weight management
interventions to promote improved outcomes during adolescence.

Keywords: obesity, adolescent, weight management, household chaos, home environment

Katherine E. Darling https://orcid.org/0000-0002-
1858-4644
Geoffrey E. Putt https://orcid.org/0000-0002-5567-

8762
Katherine E. Darling is now affiliated with the Department

of Psychiatry and Human Behavior, Alpert Medical School
of Brown University.
None of the authors have any conflicts of interest to report.

The research did not receive any specific grant from funding
agencies in the public, commercial, or not-for-profit sectors.
Kent State University requires their students to submit an
electronic copy of their master’s/doctoral thesis to their
digital archival repository so that it will be openly available,

in full, to anyone, free of charge. Portions of this article are
adapted from the dissertation of Katherine E. Darling that can
be found at http://rave.ohiolink.edu/etdc/view?acc_num=
kent1559729147579083 and here modified from the original
and presented in peer-reviewed format for the first time. A
version of this data was also presented as a virtual poster
presentation at the 2020 Society for Pediatric Psychology
Annual Conference.

Correspondence concerning this article should be
addressed to Katherine E. Darling is now at the Weight
Control and Diabetes Research Center, The Miriam Hospital,
196 Richmond Street, Providence, RI 02903, United States.
Email: katherine_darling@brown.edu

1

Clinical Practice in
Pediatric Psychology

© 2022 American Psychological Association
ISSN: 2169-4834 https://doi.org/10.1037/cpp0000434

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Obesity is a major public health concern among
adolescents in the United States, with approxi-
mately 40% of adolescents currently classified as
being overweight or obese (Skinner et al., 2018).
Obesity during adolescence is associated with a
number of health concerns and negative psychoso-
cial outcomes, as well as increased morbidity and
mortality into adulthood (Gurnani et al., 2015). De-
spite promising treatments for pediatric obesity,
many youth presenting to treatment are unsuccess-
ful in changing their weight status (Wilfley et al.,
2018). Specifically, recent data from the Pediatric
Obesity Weight Evaluation Registry (POWER)
identified an average change in percent of the 95th
percentile of body mass index (BMI) of �2.0 for
adolescents ages 12–14 years after 4–6 months of
treatment (Kumar et al., 2019). A decrease of 5%
indicates clinically meaningful change (Kumar et
al., 2019). This finding suggests that most adoles-
cents do not achieve clinically significant weight
loss even after participating in a multicomponent
weight management intervention. Data from
POWER have also identified that early BMI reduc-
tion is significantly associated with long-term
weight management success across a wide age
range (4–18 years) of children (Gross et al., 2019).
Given these findings, it is particularly important to
identify potential predictors of weight loss, includ-
ing early weight loss, among adolescents present-
ingforweightmanagement.
Prior research has focused on patient factors as

predictors of weight loss success in adolescent
weight management programs (Braet, 2006; Jela-
lian et al., 2008). These individual factors include
higher baseline BMI, older age (within childhood),
and male gender all being associated with greater
weight loss success. However, these individual-
level factors are not modifiable and cannot be
directly targeted through behavioral weight control
(BWC) interventions. The American Academy of
Pediatrics recommends involving parents in BWC
through behavioral strategies such as limit setting,
modifying the home environment, and reducing
barriers (Bean et al., 2020; Spear et al., 2007). As
children transition to adolescence, there is an
increase in autonomy and desire for independence;
however,thehouseholdenvironmentstillhasasub-
stantial impact of health behaviors (Bean et al.,
2020; Shrewsbury et al., 2011). Research to date
has not examined specific facets of the home envi-
ronment that may predict weight status and early
treatment success of adolescents seeking BWC
intervention.

Home Environment

One such aspect of the immediate home environ-
ment is food insecurity, the experience of limited or
uncertain access to food (Nord et al., 2007), which
has been related to increased rates of being over-
weight (20.8% compared to 15.6% in those without
food insecurity) among adolescents ages 12–17
years(Caseyetal.,2006).Anumberofmechanisms
have been proposed to explain this association,
including increased availability of energy-dense
foods (Drewnowski, 2004), a cycle of restriction
during times of decreased food availability leading
toovereatingwhenfoodismoreplentiful,andmeta-
bolic changes (Casey et al., 2006; Drewnowski,
2004). Clinically, food insecurity may be a key
intervention point, potentially with families receiv-
ing education about purchasing low-cost healthy
foods, to promote BWC effectiveness. However,
studiesexaminingtheassociationbetweenpediatric
obesityandfoodinsecurityinadolescencehavetyp-
ically not been conducted within the context of a
clinical sample. Instead, these studies have focused
on convenience samples and national surveys (Lar-
son & Story, 2011). Therefore, this study sought to
examine whetherfoodinsecurity maybe one aspect
of the home environment that predicts early BWC
treatmentsuccessforadolescents.
Time constraints—a lack of time to maintain

healthyeatingandexercisebehaviorsduetoworkor
other commitments—have been associated with
increased adolescent weight status and lack of
healthy eating in the family (Hearst et al., 2012; Jabs
& Devine, 2006). Specifically, time scarcity has
been associated with less healthful diet choices,
including increased consumption of convenience or
ready-prepared foods and fast food, and a decrease
in family meals and food preparation at home (Jabs
& Devine, 2006). BWC requires a significant time
investment. Families are typically asked to attend
regularappointments,makespecificandmeasurable
goals, and perform actions toward those goals
(O’Connor et al., 2017). Given the added time-
related demands associated with implementation of
BWCintervention components(e.g., timeforphysi-
cal activity, time for grocery shopping and cooking,
time for attending appointments), families with
increased time-related barriers may be less likely to
besuccessfulinearlyBWC.
Householdchaos,orthephysicalandsocialdisor-

der at home, is an additional factor likely related to
early BWC success. Chaos within the household is
indicated by running late, lack of planning, and a

2 DARLING, VAN DULMEN, PUTT AND SATO

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noisy home. A chaotic home environment has been
related to risky health outcomes for adolescents,
including increased risk for smoking, drinking, and
substance use (Chatterjee et al., 2015). A recent
overview of the literature has identified the impor-
tance of behavioral and social routines (opposite of
chaos)inthefamilytotreatingobesitythroughchild-
hood and adolescence (Hart et al., 2020). In young
children, household routines have been related to
weight status in both cross-sectional and interven-
tion research (Anderson & Whitaker, 2010; Haines
et al., 2013). Specifically, in a cross-sectional analy-
sis, exposure to higher levels of household routines
(i.e., family meals, adequate sleep, and limiting
screen time) was associated with lower prevalence
of obesity as compared to young children not
exposed to these routines (Anderson & Whitaker,
2010).Althoughthiswasanationallyrepresentative
sample taken from a cohort study, it was limited by
the use of single-item measurements for each rou-
tine.Inaddition,thiscohortstudywaslimitedbythe
inclusionofonlychildrenaged4years(Anderson&
Whitaker, 2010). In children from kindergarten to
eighth grade, fewer family routines have been
related to increased probability of childhood obesity
(Anderson, 2012). A randomized study of young
children (2–5 years) found that an intervention to
promote household routines led to decreased BMI
(Hainesetal.,2013).Researchindicatingtheimpor-
tanceofanorganizedhouseholdforpositiveweight-
related outcomes among younger children has not
yet been examined within adolescents, especially
earlyinweightmanagementtreatment.

The Current Study

The present study extends the literature on pre-
dictorsofadolescentweightstatusandearlyweight
change in the context of a hospital-based pediatric
BWC program by examining the impact of three
modifiable household factors. The first aim was to
examinethe associationbetweenhouseholdfactors
(food insecurity, time constraints, and household
chaos) and weight status at initial presentation (i.e.,
baseline). It was hypothesized that higher levels of
food insecurity, time constraints, and household
chaos would be associated with higher weight sta-
tus at baseline. The second aim was to examine the
impact of these household variables on weight sta-
tus change over the first 2 months of the interven-
tion. It was hypothesized that higher levels of food
insecurity,timeconstraints,andhouseholdchaosat
baseline would all be associated with less weight

statuschangeoverthefirst2monthsofweightman-
agementintervention.

Method

Participants and Procedures

Participants included 205 adolescents (10–18
years) presenting to a tertiary care pediatric BWC
program in the midwestern United States and their
parents/guardians.Parentsandadolescentswereel-
igible to participate if both the parent and adoles-
cent (a) spoke English fluently and (b) did not have
an identified learning disorder or cognitive disabil-
ity preventing them from completing question-
naires(perparentreport).

Procedures

Aspartofstandardclinicalcare,eachnewfamily
was mailed a packet with psychosocial measures
andbriefinformationaskingthefamilytocomplete
the measures prior to their first clinic appointment.
If patients did not complete measures prior to their
initial appointment, they were provided with an
additional copy of measures and asked to complete
them immediately prior to the first clinic appoint-
ment. Consent/assent were obtained in a private
area by trained research assistants at patients’ first
clinic visit. Psychosocial measures were collected
once, at the beginning of treatment, with anthropo-
metric data collected at each appointment within
the clinic. This study was approved by the Akron
Children’sHospitalInstitutionalReviewBoard.

Intervention

Each patient was seen by a psychologist, exercise
physiologist, dietician, and medical provider (physi-
cian or nurse practitioner) at each 2-hr appointment
within the clinic. During the intake evaluation, the
focus was on assessing current activity level, eating
patterns, and psychological factors related to their
weight status. Brief psychoeducation and goal set-
ting were conducted during each visit. Although no
treatment manual was utilized, at each appointment,
providers generally reviewed information previ-
ously presented, discussed problems or barriers that
familiesfacedrelatedtobehaviorchange,introduced
new topics related to weight loss, and set new goals
for the upcoming month. Intervention topics were
chosen with input from both providers and patients,
covering topics relevant to the adolescent while also

ROLE OF THE HOME ENVIRONMENT IN ADOLESCENT BWC 3

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allowing for collaborative session planning. Exer-
cise physiologists introduced components of physi-
calactivityappropriatefortheadolescents’leveland
provided strategies for increasing physical activity.
Dieticians focused on planning a healthy, nutritious
diet and providing feedback on food intake. Specific
self-monitoring targets varied between participants
(e.g., only tracking fruit and vegetable intake, track-
ing all consumption, tracking physical activity)
depending on treatment targets. Medical providers
reviewed lab work, which was taken at the first
appointment and when clinically indicated, and dis-
cussedpotentialhealthcomplications.Psychologists
collaborated with families to discuss specific goals
and strategies for behavioral changes suggested by
otherdisciplines(e.g.,behavioralreinforcement,set-
ting specific reasonable goals) as well as review
other behavioral strategies for weight loss (e.g.,
slowingpaceofeating,self-monitoring,contingency
reinforcement).
Families were asked to schedule appointments

approximatelyoncepermonthforatotalof6months,
with extension as appropriate for each family. Find-
ings from the present study focused on baseline mea-
surement and measurement at the adolescent’s third
appointment (approximately 2 months out from the
initial intake). This time point was selected to be con-
sistent with prior research demonstrating treatment
success at 2 months as a predictor of longitudinal
treatmentsuccess(Unicketal.,2015).

Measures

Demographics

Parents completed a demographic question-
naire concerning characteristics of the parent and
adolescent participating in the clinic. This ques-
tionnaire included items regarding both parental
and adolescent age, sex, race/ethnicity, educa-
tional attainment, as well as parental employment
status, occupation, and marital status. Demo-
graphic items (i.e., parent-report marital status,
employment status, educational attainment, and
occupation)wereusedtocalculate socioeconomic
status (SES) using the Hollingshead four-factor
index (Hollingshead, 1975). Education was coded
on a 7-point scale, and occupation was rated on a
9-point scale, with a range of total scores from 8 to
66. All calculations were conducted following the
guidelines set forth by Hollingshead (1975), with
higherscoresreflectinghigherSES.

Adolescent Weight

Adolescent height and weight were measured
objectively at each clinic appointment. Trained
staff members collected measurements while
patients were wearing light clothing and no shoes.
Weight in kilograms was measured using a Scale-
tronix digital scale, and height in centimeters was
measured using a Seca stadiometer. Measurements
were used to calculate BMI (kg/m2) at baseline and
each subsequent time point. Prior literature has
identified limitations of other commonly used met-
ricsofadolescentweightstatus(e.g.,zBMI).There-
fore,BMIandchangeinBMIoverthecourseofthe
intervention were used to measure adolescent
weight status, consistent with prior research in this
area(Grossetal.,2019).

Food Insecurity

Parent-report household food insecurity was
measured via the validated USDA Core Food Se-
curity Module—Short Form (CFSM-SF; Bickel
et al., 2000). This six-item scale measures level of
food insecurity within the past year. The CFSM-
SF was developed from the 18-item CFSM
through identification of the six indicators that
approximated the categories of the initial food se-
curity measure (Bickel et al., 2000). Affirmative
responsesaresummed,with higherscores indicat-
inghigherfoodinsecurity.Specifically,scorescan
range from 0 (food secure) to 10 (very low foodse-
curity or food insecurity with hunger). An exam-
ple item is “In the last 12 months, did you ever eat
lessthanyoufeltyoushouldbecausetherewasnot
enoughmoneytobuyfood?”Itemresponsesdiffer
between items and include “yes” and “no” (three
items); “often true,” “sometimes true,” and “never
true” (two items); and “almost every month,”
“some months but not every month,” and “only 1
or 2 months” (one item). The CFSM has been
found to be valid and reliable in previous studies
(Bickeletal.,2000).

Time Constraints

Timeconstraintswithinthefamilyweremeasured
via parent report on the time constraints subscale of
the Barriers to Pediatric Weight Management Scale
(Darling et al., 2018). This five-item subscale
assesses parents’ perceptions of their time con-
straintsinrelationtotheirabilitytoimplementhealth
family behaviors. Items were rated from 1 (strongly
disagree) to 5 (strongly agree), and a mean of all

4 DARLING, VAN DULMEN, PUTT AND SATO

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items was calculated for the overall time constraints
scorewitharangefrom1,indicatinglowertimecon-
straints, to 5, indicating higher time constraints. An
example item is “It is hard for me to find the time to
prepare healthy foods at home.” This measure has
shown good convergent validity and appropriate in-
ternal consistency within prior normative and clini-
calsamples(Darlingetal.,2020,2018).

Household Chaos

The parent-reported Confusion, Hubbub, and
Order Scale—Short Version (CHAOS) is a six-item
measure used to identify chaos and disorder within
the household (Hart et al., 2007; Matheny et al.,
1995). Parents rated items on a 5-point scale from 1
(definitelyuntrue)to5(definitelytrue).Ameanscore
of all items was calculated, with a range of scores
from 1, indicating lower chaos, to 5, indicating
higher chaos. Items on this scale capture general
chaos (four items; e.g., “It’s a real zoo in our house”
and “You cannot hear yourself think in our home”)
and routines (two items; i.e., bedtime and screen
time routines). The CHAOS scale has shown strong
psychometric characteristics and has been shown to
be valid and reliable for adolescents ages 10–18
years(Chatterjeeetal.,2015;Mathenyetal.,1995).

Data Analytic Plan

Missing data was handled using listwise dele-
tion. All models include age, sex, and SES as cova-
riates based on associations in prior literature. Sex
was coded as 0 for men and 1 for women. Tests of
normality assumptions (i.e., skew and kurtosis)
wereconductedforallvariablesofinterest.Prelimi-
nary analyses included independent-samples t tests
to examine differences on demographic variables
between adolescents presenting less than three ses-
sions to those that attended at least three sessions.
Correlationswereconductedbetweenallstudyvar-
iables and continuous demographic variables (i.e.,
ageandSES).
Hierarchical linear regression was used to test

the first aim of the study, the impact of household
factors on adolescent weight status at presentation
to treatment. Age, sex, and SES were included as
covariates in Step 1 of the model, with all three
household factors, food insecurity, household
chaos, and time constraints, entered into Step 2 of
the model to predict adolescent BMI. Similarly,
hierarchical linear regression was used to examine
the impact of the household variables on weight

change from baseline to Session 3. Paralleling Aim
1, age, sex, and SES were included as covariates in
Step 1 of the model, with the three household fac-
tors entered into Step 2 of the model to predict
changeinadolescentBMI.

Results

Preliminary Analyses

Adolescents (M age = 13.26, SD = 2.22) who
participated were primarily non-Hispanic White
(70.7%), and over half were female (59%). All
variables were normally distributed, and no
transformations were required. Missing data
ranged from 0% to 4.3%, with 16 adolescents
excluded from the final sample due to missing
data. Within the final sample, 188 adolescents
attended the first appointment, 127 attended a
second appointment (67.5%), and 97 attended a
third appointment (51.6%). Further descriptive
statistics for the sample are listed in Table1.Inde-
pendent-samples t tests were conducted to examine
differences between participants who attended less
than three appointments (i.e., dropping out prior to
the 2-month follow-up) to those that remained
engaged in treatment at the third appointment.
Nosignificant differences weredetected between
groups. Of adolescents who attended all three
appointments, 65.1% of the sample lost weight;
however, the average BMI change (M = �.23,
SD = 1.60) did not reach statistical significance
(p = .21). Of the adolescents who attended all
three appointments and lost weight, the average
BMI change was �.91 (SD = 1.26; p , .001).
Correlations between all variables can be found
in Table2.

Primary Analyses

The hierarchical linear regression model testing
Aim1examinedwhetherhouseholdvariablessignifi-
cantly predicted baseline BMI, controlling for age,
sex, and SES. Household factors significantly pre-
dicted baseline BMI. Specifically, the second step of
the regression (including all four household factors)
was statistically significant, F(3, 181) = 3.85, p =
.011, explaining 5.3% of the variance in adolescent
BMI beyond age, sex, and SES. Household chaos
wastheonlysignificantpredictorofweightstatus(p=
.007).FullregressionresultsaredisplayedinTable3.

ROLE OF THE HOME ENVIRONMENT IN ADOLESCENT BWC 5

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The hierarchical regression model testing Aim 2
foundthathouseholdfactorssignificantlypredicted
BMI change beyond age, sex, and SES, F(3, 92) =
3.03, p = .033, explaining 8.9% of the variance in
adolescent BMI change beyond age, sex, and SES.
Consistent with findings for Aim 1, household
chaos was the only significant predictor of BMI
change(p=.017).PleaseseeTable3forfullregres-
sionresults.

Discussion

Prior research has demonstrated that weight loss
earlyinpediatricobesitytreatmentisthebestpredictor
of treatment success using a national registry of
weight management programs across the United
States (Gross et al., 2019). Despite this work, prior
research has not yet examined the factors that may
promote initial treatment progress for adolescents

Table 2
Correlations and Descriptive Statistics for Study Variables

Variables 1 2 3 4 5 6 7 M SD

1. BMI at Session 1 — 35.90 6.78
2. BMI at Session 2 (N = 127) .98** — 36.66 6.50
3. BMI at Session 3 (N = 97) .97** .97** — 36.58 6.75
4. Adolescent age �.12 �.08 �.08 — 13.26 2.22
5. SES (Hollingshead four-factor index) �.15* �.17 �.15 .04 — 37.08 15.66
6. Family time constraints .03 �.03 .04 .19* .15* — 2.69 .82
7. Food insecurity (Core Food Security Module) .13 .12 .14 �.11 �.27** .00 — 1.05 1.78
8. Household chaos .23* .21* �.17 .19* .02 .38** �.05 3.42 .67
Note. N = 188 unless otherwise noted. BMI = body mass index; SES = socioeconomic status.
*p , .05. **p , .01.

Table 1
Descriptive Characteristics for Adolescent and Parent Demographic Variables

Characteristics N (or M) % (or SD)

Adolescent characteristics
Biological sex
Female 111 57.1%
Male 77 42.9%

Ethnicity
Hispanic or Latino 5 2.7%
Not Hispanic or Latino 169 89.9%
Don’t know/declined to respond 14 7.4%

Race
White/Caucasian 133 70.7%
Black/African American 29 15.5%
Other/don’t know 30 13.4%

Age M = 13.26 SD = 2.22
BMI at Session 1 M = 35.90 SD = 6.78
BMI at Session 2 (N = 127) M = 36.66 SD = 6.50
BMI at Session 3 (N = 97) M = 36.57 SD = 6.75

Parent characteristics
Biological sex
Female 163 86.7%
Male 22 11.7%
Declined to respond 3 1.6%

Education (of clinic-attending parent)
Did not complete high school 8 4.1%
High school graduate 57 29.3%
Partial college (at least 1 year) or specialized training 59 27.7%
Standard college or university graduation 49 25.0%
Graduate professional training (graduate degree) 23 12.2%

Note. All percentages may not equate to 100 due to rounding. N = 188 unless otherwise
noted. BMI = body mass index.

6 DARLING, VAN DULMEN, PUTT AND SATO

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participating in a hospital-based BWC program. This
is especially important to identify clinical targets for
earlyinterventiontopromoteimprovedtreatmentsuc-
cessoverthefirstfewsessions.
Household chaos was the only significant pre-

dictor of both baseline weight status and early
treatment success. Chaos within the household,
characterized by high levels of disorganization,
background stimulation, lack of family routines,
and absence of predictability in the home, may
impede sustained health-related behaviors. De-
spite the demonstrated importance of household
routines (e.g., mealtime, screen time, bedtime) on
weight status in preschool- and school-age chil-
dren (Anderson et al., 2017; Anderson & Whi-
taker, 2010; Haines et al., 2013) the importance of
routines and stability (which minimize chaos in
the household) has been widely ignored as chil-
dren transition into adolescence. Expanding upon
prior work in adolescents relating a chaotic home
environment to risky health outcomes (Chatterjee
et al.,2015),thisstudy isthe first tolink household
chaos to clinical BWC outcomes for adolescents.
Further, the present study focuses on general
chaos in the household, which may be a more
accurate assessment of the broader family envi-
ronmentascomparedtoaspecificmeasuresuchas
householdroutines.
Beyondinterventionsfocusedonhouseholdrou-

tines, a recent scoping review identified an absence
of interventions with the primary aim of addressing

household chaos (Marsh et al., 2020). Clinicians
and clinical researchersshould considerfocallytar-
geting both general household chaos and routines
within initial sessions of weight management inter-
vention to increase the likelihood that families are
able to engage in other weight management strat-
egies (e.g., self-monitoring, stimulus control). For
someyouthseekingweightmanagement,clinicians
may consider working with families to identify the
underlying causes of chaos in their home and de-
velopfamily-specificstrategiestodecreasingchaos
earlyinBWC.
Contrary to hypotheses in the present study, nei-

ther food insecurity nor time constraints were
related to either baseline weight status or weight
change early in treatment. Although both of these
household factors were included in the present
study due to their identified associations with pedi-
atric weight status (Casey et al., 2006; Hearst et al.,
2012), these associations were not identified within
the present study. Prior research concerning food
insecurityandweightstatusinadolescentshasbeen
mixed. Although some studies have identified an
association (Casey et al., 2006), others have found
that the prevalence of overweight/obesity are high
in adolescents with food insecurity, despite no
direct association between these variables (Eisen-
mann et al., 2011). Further, although time con-
straints have been associated with adolescent
weight status (Hearst et al., 2012), this has not been
explored in the context of BWC. Prior work
<

Statistics homework help

Names

Patient # Infectious Disease Age
1 Yes 69
2 Yes 35
3 Yes 60
4 Yes 55
5 Yes 49
6 Yes 60
7 Yes 72
8 Yes 70
9 Yes 70
10 Yes 73
11 Yes 68
12 Yes 72
13 Yes 74
14 Yes 69
15 Yes 46
16 Yes 48
17 Yes 70
18 Yes 55
19 Yes 49
20 Yes 60
21 Yes 72
22 Yes 70
23 Yes 76
24 Yes 56
25 Yes 59
26 Yes 64
27 Yes 71
28 Yes 69
29 Yes 55
30 Yes 61
31 Yes 70
32 Yes 55
33 Yes 45
34 Yes 69
35 Yes 54
36 Yes 48
37 Yes 60
38 Yes 61
39 Yes 50
40 Yes 59
41 Yes 60
42 Yes 62
43 Yes 63
44 Yes 53
45 Yes 64
46 Yes 50
47 Yes 69
48 Yes 52
49 Yes 68
50 Yes 70
51 Yes 69
52 Yes 59
53 Yes 58
54 Yes 69
55 Yes 65
56 Yes 61
57 Yes 59
58 Yes 71
59 Yes 71
60 Yes 68

Statistics homework help

Pastas R Us, Inc.

Pastas R Us, Inc. 5

Pastas R Us, Inc.

David Leonard

University of Phoenix

DAT/565

May 7, 2022

Scope and descriptive statistics

 Restaurant data analytics is the process of analyzing every data point related to a business and converting them into meaningful insights, which can help improve everything from menus and staff straining to restaurant policies and marketing campaigns. Larger restaurants may even have 8 or more technology vendors on their payroll, which highlights the need to invest in a reliable analytics solution. Restaurants that operate on this scale, think McDonalds scale, may be looking at big solutions to understand and make use of the huge amount of data they generate.

Objective

The main objective of this research is to undertake data analysis in order to:

I. Understand whether the current expansion criteria can be improved.

II. evaluate the effectiveness of the Loyalty Card marketing strategy

III. identify feasible, actionable opportunities for improvement

The variables that were used in the analysis include the size of the restaurant in square feet, the average spending of an individual in a restaurant, the sales growth over the previous years, the loyalty card percentage of the net sales, annual sales per sq. ft., median income and median age.

The descriptive analysis

Column1


Obs


SqFt


Sales/Person


Sales Growth%


LoyaltyCard%


Sales/SqFt


BachDeg%

Mean

37.5

2580.473

7.044054054

7.4140541

2.026486

420.3054054

26.31081081

Standard Error

2.5

43.58345

0.034555901

0.7701093

0.064212

15.95377053

0.814285102

Median

37.5

2500

7

7.03

2.075

396.01

26.5

Mode

#N/A

2500

7.03

4.05

2.04

#N/A

29

Standard Deviation

21.50581

374.919

0.2972611

6.6247303

0.552371

137.2395233

7.004745311

Sample Variance

462.5

140564.3

0.088364161

43.887052

0.305114

18834.68676

49.06645687

Kurtosis

-1.2

3.760921

0.85439895

1.146166

1.4536

2.880513142

-0.937297935

Skewness

1E-16

0.527171

0.903631503

0.4937475

-0.756891

1.23589655

0.140544196

Range

73

2548

1.43

37.12

3.09

808.56

26

Minimum

1

1251

6.54

-8.31

0.29

178.56

14

Maximum

74

3799

7.97

28.81

3.38

987.12

40

Sum

2775

190955

521.26

548.64

149.96

31102.6

1947

Count

74

74

74

74

74

74

74

The total count of the data that were used in this case was 74 as indicated from the descriptive analysis table above. Most of the sizes of the restaurants are around 2580 square feet and the sales percentage growth mean is 7.4 while the mean for sales per person is 7.0. The mean for the company sales per square is 420.30.

Analysis

Scatter plot of BachDeg% versus Sales/SqFt

The type of relationship that exist in this case is a positive relationship. This is because as the X-values increase (move right), the Y-values tend to increase (move up). excluding outliers, we can see that the X axis increases as the Y axis increases. The sales per size of the restaurant increases as the BachDeg increases.

Scatter plot for Med Income versus Sales/SqFt

The type of relationship that exist in this case is a positive relationship. This is because as the X-values increase (move right), the Y-values tend to increase (move up). excluding outliers. However, the data are scattered at the center and there is no huge increase on the X axis. This means the med income the increases steadily against the sales per square

Scatter Plot MedAge versus Sales/SqFt

In this case there is no relationship that exist.

LoyaltyCard (%) versus SalesGrowth (%)

The type of relationship that exist in this case is a positive relationship. This is because as the X-values increase (move right), the Y-values tend to increase (move up). excluding outliers

Recommendations and implementation

Based on the assessment above BachDeg% versus Sales/SqFt correlates and it is more effective. It shows that as the med income increases the size of the restaurant increases. Additionally, according to Scatter Plot MedAge versus Sales/SqFt, it shows that there is identified relationship between median age and the sales square per feet. It can be justified through use of line graph

The median age remains constant as the sales per square feet rise and fall which is a clear indication that there is no statistical relationship between the two. The loyalty card and the sales growth correlates.

Recommendations

The company should change the marketing strategy basing on % w/ Bachelor’s Degree (3 Miles) and the sales per square feet. Just like the loyalty card and the sales per square feet are correlated they should invest on the marketing strategies to increase the income of the restaurant

Instead of the company targeting the entire market they should focus on young people having the age of 35 years old. Since most of them having the age of 34 prefer having their services within the restaurant. The company implementing this strategy and committing their energy with this specific defined group with the market will help in improving their sales.

In a restaurant, collecting data is a bit easy as compared to other places. The most important thing to consider is identification cards. Identification may be a passport or a national identity card. Apart from acquiring the phone number and their address. Having this information will provide an endless opportunity for targeted marketing. Some of the POS systems allows the restaurant to access the demographic data of their customers and if they find missing data they can be filled using the public records.

References

Loeb, S., Dynarski, S., McFarland, D., Morris, P., Reardon, S., & Reber, S. (2017). Descriptive Analysis in Education: A Guide for Researchers. NCEE 2017-4023. National Center for Education Evaluation and Regional Assistance.

Mavridou, A. M., Bergmans, L., Barendregt, D., & Lambrechts, P. (2017). Descriptive analysis of factors associated with external cervical resorption. Journal of endodontics43(10), 1602-1610.

LoyaltyCard(%) versus SalesGrowth(%)

LoyaltyCard% -8.31 -4.01 -3.94 -3.39 -3.3 -1.94 -0.77 -0.37 -0.25 -0.17 0.47 0.55000000000000004 0.77 1.92 2.0499999999999998 2.12 2.84 2.88 3.96 4.04 4.05 4.05 4.24 4.58 5.09 5.14 5.48 5.86 5.91 5.98 6.08 6.08 6.13 6.27 6.57 6.9 6.94 7.12 7.39 7.67 7.91 8.08 8.27 8.5399999999999991 8.58 8.7200000000000006 8.75 8.7899999999999991 8.9 9.1199999999999992 9.4700000000000006 10.17 10.66 10.97 11.34 11.45 11.51 11.73 11.83 11.95 12.47 12.8 13.78 14.09 14.23 14.6 14.88 15.42 16.18 17.23 18.43 20.76 25.54 28.81 2.0699999999999998 2.54 1.66 2.06 2.48 2.96 2.2799999999999998 2.34 2.2000000000000002 2.34 2.09 2.4700000000000002 2.04 2.02 2.0099999999999998 2.64 2.2200000000000002 2.0699999999999998 1.94 2.17 0.72 2 1.81 2.13 2.5 2.63 1.95 2.04 1.41 2.0499999999999998 2.13 2.08 2.73 1.95 2.04 1.62 1.95 1.64 1.78 2.23 2.15 2.83 2.37 3.07 2.19 1.28 1.76 2.5099999999999998 1.9 1.98 2.41 2.17 2.16 0.28999999999999998 1.85 1.88 2.19 2.56 2.16 2.1 1.98 0.87 1.07 3.38 1.17 2.14 0.93 2.2200000000000002 1.68 2.41 2.81 1.0900000000000001 0.64 1.77

Sales/SqFt 701.97 209.93 364.92 443.04 399.2 264.64 571.59 642.25 461.45 638.82000000000005 484.38 581.09 267.70999999999998 572.84 586.48 368.73 351.47 458.24 987.12 357.45 405.77 680.8 368.02 303.95 393.9 562.12 494.88 310.07 373.46 235.81 413.08 625.22 274.3 542.62 178.56 375.33 329.09 297.37 323.17 468.84 352.57 380.34 398.12 312.14999999999998 452.16 698.64 367.19 431.93 367.06 400.53 414.36 481.11 538.05999999999995 330.48 249.93 291.87 517.4 551.58000000000004 386.81 427.5 453.94 512.46 345.27 234.04 348.33 348.47 294.95 361.14 467.71 403.78 245.74 339.94 400.82 326.54000000000002 MedAge 34.4 41.2 40.299999999999997 35.4 31.5 36.299999999999997 35.1 37.6 34.9 34.799999999999997 36.200000000000003 32.200000000000003 30.9 37.700000000000003 34.299999999999997 32.4 32.1 31.4 30.4 33.9 35.6 35.9 33.6 37.9 40.6 37.700000000000003 36.4 40.9 35 26.4 37.1 30.3 31.3 29.6 32.9 40.700000000000003 29.3 37.299999999999997 39.799999999999997 33.9 35 35 35.9 33 30.9 38.5 40.5 32.1 34.799999999999997 38 37 34.700000000000003 36.4 36.799999999999997 32.200000000000003 34.799999999999997 36.700000000000003 33.799999999999997 34.200000000000003 39 34.9 39.299999999999997 35.6 36 41.1 24.7 40.5 32.9 30.3 36.200000000000003 32.4 43.5 41.6 31.4

BachDeg/Sales/SqFt

Sales/SqFt 31 20 24 29 18 30 14 33 28 29 39 23 22 37 24 17 37 22 36 34 26 20 20 26 21 37 34 34 30 16 28 36 18 36 18 24 22 29 25 28 40 39 30 17 22 29 19 29 18 19 34 25 30 21 30 30 28 31 16 31 40 33 28 23 16 25 25 18 15 19 27 21 29 15 701.97 209.93 364.92 443.04 399.2 264.64 571.59 642.25 461.45 638.82000000000005 484.38 581.09 267.70999999999998 572.84 586.48 368.73 351.47 458.24 987.12 357.45 405.77 680.8 368.02 303.95 393.9 562.12 494.88 310.07 373.46 235.81 413.08 625.22 274.3 542.62 178.56 375.33 329.09 297.37 323.17 468.84 352.57 380.34 398.12 312.14999999999998 452.16 698.64 367.19 431.93 367.06 400.53 414.36 481.11 538.05999999999995 330.48 249.93 291.87 517.4 551.58000000000004 386.81 427.5 453.94 512.46 345.27 234.04 348.33 348.47 294.95 361.14 467.71 403.78 245.74 339.94 400.82 326.54000000000002

MedIncome/sales/SqFt

MedIncome 701.97 209.93 364.92 443.04 399.2 264.64 571.59 642.25 461.45 638.82000000000005 484.38 581.09 267.70999999999998 572.84 586.48 368.73 351.47 458.24 987.12 357.45 405.77 680.8 368.02 303.95 393.9 562.12 494.88 310.07 373.46 235.81 413.08 625.22 274.3 542.62 178.56 375.33 329.09 297.37 323.17 468.84 352.57 380.34 398.12 312.14999999999998 452.16 698.64 367.19 431.93 367.06 400.53 414.36 481.11 538.05999999999995 330.48 249.93 291.87 517.4 551.58000000000004 386.81 427.5 453.94 512.46 345.27 234.04 348.33 348.47 294.95 361.14 467.71 403.78 245.74 339.94 400.82 326.54000000000002 45177 51888 51379 66081 50999 41562 44196 50975 72808 79070 78497 41245 33003 90988 37950 45206 79312 37345 46226 70024 54982 54932 34097 46593 51893 88162 89016 114353 75366 48163 49956 45990 45723 43800 68711 65150 39329 63657 67099 75151 93876 79701 77115 52766 32929 87863 73752 85366 39180 56077 77449 56822 80470 55584 78001 75307 76375 61857 61312 72040 92414 92602 59599 72453 67925 42631 75652 39650 48033 67403 80597 60928 73762 64225

MedAge versus Sales/SqFt

MedAge 701.97 209.93 364.92 443.04 399.2 264.64 571.59 642.25 461.45 638.82000000000005 484.38 581.09 267.70999999999998 572.84 586.48 368.73 351.47 458.24 987.12 357.45 405.77 680.8 368.02 303.95 393.9 562.12 494.88 310.07 373.46 235.81 413.08 625.22 274.3 542.62 178.56 375.33 329.09 297.37 323.17 468.84 352.57 380.34 398.12 312.14999999999998 452.16 698.64 367.19 431.93 367.06 400.53 414.36 481.11 538.05999999999995 330.48 249.93 291.87 517.4 551.58000000000004 386.81 427.5 453.94 512.46 345.27 234.04 348.33 348.47 294.95 361.14 467.71 403.78 245.74 339.94 400.82 326.54000000000002 34.4 41.2 40.299999999999997 35.4 31.5 36.299999999999997 35.1 37.6 34.9 34.799999999999997 36.200000000000003 32.200000000000003 30.9 37.700000000000003 34.299999999999997 32.4 32.1 31.4 30.4 33.9 35.6 35.9 33.6 37.9 40.6 37.700000000000003 36.4 40.9 35 26.4 37.1 30 .3 31.3 29.6 32.9 40.700000000000003 29.3 37.299999999999997 39.799999999999997 33.9 35 35 35.9 33 30.9 38.5 40.5 32.1 34.799999999999997 38 37 34.700000000000003 36.4 36.799999999999997 32.200000000000003 34.799999999999997 36.700000000000003 33.799999999999997 34.200000000000003 39 34.9 39.299999999999997 35.6 36 41.1 24.7 40.5 32.9 30.3 36.200000000000003 32.4 43.5 41.6 31.4

Statistics homework help

Tolerancing

Exercise

• Ten blocks are stacked on top of each other

• The Specification for the stack is 100 +/- 10

• What is the specification for an individual block?

• Simulate the results assuming
• Normal distribution with Cpk of 1.33

• What specification is required if a Cpk of 1.33 is desired?
• What could cause this to be incorrect?

Exercise – Strain Energy in a Solid Shaft

• Units

• U = Strain energy due to
torsion

• T = torque

• L = length

• G = shear modulus

• r = radius

• Inputs

• T = normal, mean = 2000

• L = normal, mean = 100

• G = normal, mean = 994718.4

• r = normal, mean = 4

• Question

• 0.46 < U < 0.54

• Process s for T is 11

• Process s for L is 0.53

• Determine specifications
for each input

• Allocate variance equally
given no process
information

• Compare to worst case
tolerance

4

2

rG

LT
U


=

Useful Practices for Input Variation

• Inputs from production variation

• Estimate variation statistically

• Identify the shape of the distribution from process knowledge

• Assume that long-term, there will be more variation than what is typically
measured in a short-term data collection

• Inputs representing a range of usage

• Assume the worst case can happen

• Analyse at the extremes of the conditions

• Treat it as a mean shift and not as a random variable

• Inputs representing aging or deterioration

• Assume the worst case can happen

• Analyse at the extremes of the conditions

• Treat it as a mean shift and not as a random variable

Useful Practices for Input Variation – Examples

• Example production variation

• A device dispenses a coating material,

• The volume of material is affected by its heater temperature,

• The temperature is centered by computer control,

• Average temperature is 35°C, standard deviation is 1°C,

• Analyse with temperature as a normal distribution.

• Example range of usage

• A car radio is expected to work from -20°C to 120°C

• Analyze the radio performance twice, once at each temperature extreme

• Don’t treat temperature as a random variable with a uniform distribution

• This would assume you are designing for an “average” environment, with
occasional excursions to the extremes,

• In fact, you are covering the full range of expected usage conditions.

Useful Practices for Input Variation – Examples
• Example aging or deterioration

• The performance of a capacitor will degrade over time,

• Supplier expects 13% loss in capacitance over the life,

• The manufacturing tolerance is ±5%,

• Supplier’s capability is Ppk=2.0, s=5%/6 = 0.83%

• Do statistical analysis twice, at the extremes of capacitance:

• Statistical tolerance for new parts at nominal capacitance and
s = 0.83%

• Statistical tolerance for aged parts at deteriorated capacitance and
s = 0.83%

Statistics homework help

Example 5.6

Test Duration Calculation for Zero Failure testing with the Weibull Distribution
Sample size = 8
Required Reliability = 95.00%
Required Time = 150.000
Confidence Level = 90.0%
Shape Parameter = 1.4
Test Duration = 514.2067403175
True L5 Life 450.000
True Scale Parameter = 3,754.90
Probability of Passing the Test = 61.0%
Test Duration for Testing With 1 Failure
Failure Time of Initial Test Sample = 1.82
Remaining # of Samples = 7
Reliability = 95.00%
Required Time = 150
Confidence Level = 90.0%
Shape Parameter = 1.4
Chi-Square Critical Value = 7.7794403397
Test Duration = 822.615426708
True L95 Life 450
True Scale Parameter = 3,754.90
Probability of Passing the Test = 77.5%

Statistics homework help

Article Summary Instructions

Due Date: Sunday, May 8th at 5 pm

Points: 30 points

Submit your assignment as a Word document or pdf to the link on Canvas

For this assignment, you will find a kinesiology article within your area of interest. The article must have been published within the last 10 years in a peer-reviewed academic journal. You must use a quantitative article for this assignment (
NOT a review or thesis
). You must use three search
terms
to find your article. You will read the article and use it to answer the questions outlined below.

Note: You need a quantitative, peer-reviewed article
NOT
a qualitative article, review, or thesis. Quantitative articles are typically around 7-30 pages, the researchers will collect their own data by giving their participants quantitative tests, and the researchers will run statistical analyses.

Label your answers clearly as Part 1, Part 2, etc.

1. Name the database you used to find your article. (1 point)

2. Name the three search terms you typed into the database to find the article you selected for this assignment. (3 points)

3. Include the reference for your article in correct APA format (6th edition). (5 points)

4. Name the author’s purpose of the study. Write the purpose as a statement. If you write the purpose directly as the authors have it, include it in quotes and include an in-text APA citation. Note: The authors may have more than one purpose (you can choose one). (2 points)

5. State whether the authors research question/ hypothesis is a difference or relationship type of question, or if they looked at both differences and relationships. (1 point)

6. Identify TWO variables used in your study. (If your study has more than two variables, choose two, and ONLY report those two variables. Do NOT name more than two variables.) Report the scale of measurement for both variables (nominal, ordinal, interval, or ratio). (4 points)

7. In a single sentence, report TWO tests they used to collect data (2 points) and state what those two tests were used to measure in the study. (2 points)

8. In a single sentence, report all the statistical analysis(ses) they used in their study. Note: The statistical analysis they use will be at the end of the Methods section/ beginning of Results section. (2 points) Report how the authors visually displayed their results (i.e. a graph, a table, figures, etc.). (2 points)

9. Report the key findings from the study
in your own words
in at least three sentences (what is the takeaway message from their results or beginning of discussion section). This section should be in your own words, do NOT include quotes or use the articles exact words. (3 points)

10. Discuss which section of the research article you found most challenging to understand and why. You must name at least ONE challenge you had to get the point. (1 point)

11. Include a pdf of the article on Canvas with your assignment submission. (2 points)

DO NOT use either of the following articles as they were used as examples/ demonstrations. If you use either of these articles, you will receive a zero for the assignment.

Spink, K. S., McLaren, C. D., & Ulvick, J. D. (2018). Groupness, cohesion, and intention to return to sport: A study of intact youth teams. International Journal of Sports Science & Coaching, 13(4), 545-551.

Lange, E., Kucharski, D., Svedlund, S., Svensson, K., Bertholds, G., Gjertsson, I., & Mannerkorpi, K. (2019). Effects of aerobic and resistance exercise in older adults with rheumatoid arthritis: a randomized controlled trial. Arthritis Care & Research71(1), 61-70.

Statistics homework help

Option 1

MTH 245 DATA ANALYSIS PROJECT (Body Temperature in degrees Farenheit) – 1A and 1B
Written Summary 35
The student demonstrates an understanding of key concepts and adequately address all aspects of this analysis assignment. The assignment report is submitted as a formal paper in paragraph form and is well written with full sentences, and is typed and well formatted with appropriate grammar, spelling, and punctuation.
* Brief introductory paragraph regarding the background of data.
* Specified the shape of the distribution of the data and referenced graph(s) used to make decision.
* Discussed the presence or absence of outliers.
* Discussed which measure of center was most appropriate (the values of mean, median, and mode) within context.
* Interpreted the mean and standard deviation in context of the data.
*commented on the assessment of normality (QQ plot)
*Commented on which test to use and why (z-test or t-test)
Interpret results of statistical analysis using context of data. – separate points below
Inferential Analysis – Confidence Interval and Full Hypothesis Test (Significance Test) 20
Stated the practical interpretation for the XX% confidence interval within context. 5
Correct null hypothesis 2
Correct alternative hypothesis 2
Correct p-value 2
Correct decision: {Reject H0, Do not reject H0} 2
Correct basis for decision: (comparison of p-value to α) 2
Correct conclusion in context 3
Compared the results of the CI and hypothesis test-matched or not and why? 2
Statistical Package Output 40
Stem and Leaf Diagram (with appropriate title) 4
Histogram 2
* class limits on horizontal axis 2
* appropriately titled graph and titled axes 2
Box and Whiskers Plot (with appropriate title for graph and data axis) 4
used fences to identify outliers 1
Descriptive Statistics 10
* in table form 1
* number of observations 1
* mean 2
* median 2
* mode 2
* sample standard deviation 2
Inferential Techniques 15
QQ Plot (with appropriate tile for graph and data axis) 5
Interval bounds for two-sided CI for µ 5
Results of statistical test of hypothesis 5
Format 5
* Title page with appropriate title, name, course number and section number
* Summary
* Statistical software output for graphical summaries
* Statistical software output for numerical summaries
* Statistical software output for inferential techniques
* Complete significance test
* Sources/References – if applicable
TOTAL POSSIBLE POINTS 100
COMMENTS:

Statistics homework help

Tolerancing

Exercise

• Ten blocks are stacked on top of each other

• The Specification for the stack is 100 +/- 10

• What is the specification for an individual block?

• Simulate the results assuming
• Normal distribution with Cpk of 1.33

• What specification is required if a Cpk of 1.33 is desired?
• What could cause this to be incorrect?

Exercise – Strain Energy in a Solid Shaft

• Units

• U = Strain energy due to
torsion

• T = torque

• L = length

• G = shear modulus

• r = radius

• Inputs

• T = normal, mean = 2000

• L = normal, mean = 100

• G = normal, mean = 994718.4

• r = normal, mean = 4

• Question

• 0.46 < U < 0.54

• Process s for T is 11

• Process s for L is 0.53

• Determine specifications
for each input

• Allocate variance equally
given no process
information

• Compare to worst case
tolerance

4

2

rG

LT
U


=

Useful Practices for Input Variation

• Inputs from production variation

• Estimate variation statistically

• Identify the shape of the distribution from process knowledge

• Assume that long-term, there will be more variation than what is typically
measured in a short-term data collection

• Inputs representing a range of usage

• Assume the worst case can happen

• Analyse at the extremes of the conditions

• Treat it as a mean shift and not as a random variable

• Inputs representing aging or deterioration

• Assume the worst case can happen

• Analyse at the extremes of the conditions

• Treat it as a mean shift and not as a random variable

Useful Practices for Input Variation – Examples

• Example production variation

• A device dispenses a coating material,

• The volume of material is affected by its heater temperature,

• The temperature is centered by computer control,

• Average temperature is 35°C, standard deviation is 1°C,

• Analyse with temperature as a normal distribution.

• Example range of usage

• A car radio is expected to work from -20°C to 120°C

• Analyze the radio performance twice, once at each temperature extreme

• Don’t treat temperature as a random variable with a uniform distribution

• This would assume you are designing for an “average” environment, with
occasional excursions to the extremes,

• In fact, you are covering the full range of expected usage conditions.

Useful Practices for Input Variation – Examples
• Example aging or deterioration

• The performance of a capacitor will degrade over time,

• Supplier expects 13% loss in capacitance over the life,

• The manufacturing tolerance is ±5%,

• Supplier’s capability is Ppk=2.0, s=5%/6 = 0.83%

• Do statistical analysis twice, at the extremes of capacitance:

• Statistical tolerance for new parts at nominal capacitance and
s = 0.83%

• Statistical tolerance for aged parts at deteriorated capacitance and
s = 0.83%

Statistics homework help

Chapter 1

Introduction

Learning Objectives (1 of 2)

Define biostatistical applications and their objectives

Explain the limitations of biostatistical analysis

Compare and contrast a population and a sample

Explain the importance of random sampling

Learning Objectives (2 of 2)

Develop research questions and select appropriate outcome variables to address important public health problems

Identify the general principles and explain the role and importance of biostatostistical analysis in medical, public health, and biological research

What Is Biostatistics? (1 of 2)

Application of statistical principles to medical, public health, and biological applications

Collecting, summarizing, and interpreting information and

Making inferences that appropriately account for uncertainty

What Is Biostatistics? (2 of 2)

Population

(unknown information)

Sample

Summarize sample

Make inferences about Population

Issues and Limitations (1 of 2)

Must clearly define research question

Must choose appropriate study design (i.e., the way in which data are collected)

Must select a sufficiently large, representative sample

Must carefully collect and summarize data

Issues and Limitations (2 of 2)

Must quantify uncertainty

Must appropriately account for relationships among characteristics

Must limit inferences to appropriate population

Important Questions

H1N1 outbreak

Risk factors for heart disease

Drug safety and efficacy

High-risk health behaviors

Genetic determinants of disease

Risk factors for autism

Impact of diet and exercise on health

Impact of Gulf oil spill on health

Issues for Biostatisticians (1 of 2)

Children: Obesity, immunizations, asthma, autism, etc.

Adolescents: Alcohol and tobacco use, depression, STDs, traffic accidents, etc.

Adults: Cancer, CVD, substance abuse, HIV/AIDS, mental health, etc.

What is number one killer of men and women in United States?

What are the risk factors?

Issues for Biostatisticians (2 of 2)

Research question

Study sample

Sample size

Analytic techniques

Inferences—cause/effect

Limitations

Types of Studies

Laboratory studies

Animal studies

Clinical studies

Observational studies

Experimental trials

Research Teams

Principal investigator

Biostatistician

Co-investigators

Project manager

Statistical programmers

Research assistants

Biostatistician’s Role on Team

Study design

Research question

Study sample

Sample size

Enrollment/follow-up strategies

Ongoing monitoring

Interim and final analysis

Reporting of results

Careers

Pharmaceutical industry

Government

Academia

Health insurance

Demand far exceeds supply of qualified biostatisticians today.

Training/Skills

Mathematics background

Biostatistics/statistics

Public health/biology

Computer skills

Communication skills

Analytic skills

Organizational skills

Attention to detail

Statistics homework help

Robust Design for
Products & Processes

Variation influence on the Optimum

2

Input

O
u
tp

u
t

Upper Specification Limit

Save SideShow Bob’s life

2000 feet

Pool is 200 feet long
Copyright the Simpsons

Engineering

• r = range

• V = velocity

• q = angle (radians)

• g = acceleration due
to gravity (32.2 ft/s2)

( ) 
g

2sinV
r

2
θ

=
Objectives

• Target range (r) is 2000 feet

• Minimise variation of range
(less than 100 feet)

Response Sensitivity

0 10 20 30 40 50 60 70 80 90

Angle

D
is

ta
n

ce

Smaller spread

Spread in distance

Distribution Moments


−
== dxxxfxE )()(

  2222 )()()()( −=−= 

−
dxxfxxExExV

Transformations

( ) 
dy

dw
ywfyg =)( (3.1)

where: f (x) is the probability density function for x,

y = u(x) is the transformation function, and

x = w(y) is the inverse of the transformation function, and has only one root.

Example
y x= +4 12

x

y
=

−12

4

dx

dy
=

1

4

The exponential probability density function is

f x e
x

( ) =


, x > 0

Substituting into Equation 3.Error! Bookmark not defined. gives

( ) 




=

−−

4

1
)(

4/)12( y
eyg


 , y > 12

The exponential probability density function is

f x e
x

( ) =


, x > 0

Substituting into Equation 3.Error! Bookmark not defined. gives

( ) 




=

−−

4

1
)(

4/)12( y
eyg


 , y > 12

Transformations

( )
2111

, xxuy = and ( )
2122

, xxuy = . If the inverse of the transformation functions,

x w y y
1 1 1 2
= ( , ) and x w y y

2 2 1 2
= ( , ) have single roots, the joint probability density

function for y1 and y2 is

( ) ( ) Jyywyywfyyg
21221121

,,,),( = (3.1)

where J is the Jacobian and is defined as the determinant of the partial derivatives;

J
x y x y

x y x y
=
   

   

1 1 1 2

2 1 2 2

/ /

/ /

System characteristics
• Properties of means and variances of functions of

several variables, where y = f(x1, x2, x3, …, xn).

• An approximation for the mean of a function of several
variables is:

• An approximation for the variance of a function of
several variables is:

2

x

2
n

1i i

2

y
ix

y
V(y) σσ 






= 

=


=



+=

n

1i

2

x2

i

2

y
ix

y

2

1
yE(y) σμ

Circuit Example

P = V2/R

• Voltage (V) is Normally distributed
• mean = 12

• standard deviation = 0.1

• Resistance (R) is Normally distributed
• mean = 2

• standard deviation = 0.2

Where does input data come from?

• Current production
• Supplier
• Discuss how to obtain mean and standard deviation for

voltage and resistance

Circuit Example
1. What does the power distribution look like?

• Specifications

• 72 ± 10

• Will this circuit design meet specifications?

2. Change standard deviation of voltage to 0.3 and
standard deviation of resistance to 0.4

• What is the mean and standard deviation of power?

3. Change standard deviation of voltage to 0.5 and
standard deviation of resistance to 0.6

Statistical Bias

0

100

200

300

400

500

600

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10

Resistance

P
o

w
e

r
Resistance decreased from 1.0 to 0.5

Power increased from 144 to 288

Power change = 144

Resistance increased from 1.0 to 1.5

Power decreased from 144 to 96

Power change = 48

Statistical Bias

0

20

40

60

80

100

120

0 2 4 6 8 10 12 14 16 18 20

Length

W
e

ig
h

t

Length increases from 9 to 10

Weight increases from 58.7 to 64.57

Weight change = 5.87

Length decreases from 9 to 8

Weight decreases from 58.7 to 52.83

Weight change = 5.87

Circuit Example

• Use robustness approximations to compute
• Statistical bias

• Power standard deviation

• How do these results compare to the simulation?

Example
Y = 25 + 200P – 2P2 + 14T

1. Determine bias of Y & STD of
Y using robustness equations
& verify with simulation

• P = 0
• Y = 7000

2. Determine values of T & P
that minimize the STD of Y
using robustness equations &
verify with simulation

• Y = 7000

T = Normal (std = 10)

P = Normal (std = 5)

Example – Optimise using derivatives
• Y = 25 + 200P – 2P2 + 14T

• Determine T and P

• Y = 7000

• Minimise variation of Y

( ) ( ) 22222

2

T

2

2

P

2

140101454P200

T

Y

P

Y
V(y)

=+−=






+




= σσ

( ) ( )

( ) 5054
2

1

T

Y

P

Y

2

1
Bias

2

2

T2

2
2

P2

2

−=−=








+


= σσ

4P200
P

Y
−=

( )
4

P

Y
2

2

−=

14
T

Y
=

( )
0

T

Y
2

2

=

1st Order Der. P =

1st Order Der. T =

2nd Order Der. P =

2nd Order Der. T =

Example – Optimise using derivatives

Excel > Tools > Solver

T & P optimised by Solver
with minimal StD(Y)

• Friction factor (f) 0.01 < f < 0.05

• Pipe diameter (d) 0.5 < d < 10.0

• Flow rate (v) 7 < v < 50

• Pipe length (L) 2000

• Discharge level below reservoir surface (D) 25 < D < 500

• Specification 5 < HP < 45

• Friction factor (f) StDev = 0.002

• Pipe diameter (d) StDev = 0.1

• Flow rate (v) StDev = 2

• Pipe length (L) StDev = 1

• Discharge level below reservoir surface (D) StDev = 3

• HorsePower within specifications and minimise variance of HorsePower

Robustness example – Reservoir flow

D−+=
2323

0006188.0000115.000000961.0 vddfLvdvHP

Class exercise – Salt tank mixing

• Q = grams of salt after t minutes

• Tank volume (V): 500 litres max

• Salt density (d): 260 grams/litre max

• Water flow (f) litres/min: (V/5) maximum, 0.1 minimum

• Fresh water in, uniform stirring, mixed water out

• Required

• More than 90 g of salt after 2 minutes

• Between 70 g and 80 g of salt after 5 minutes

• Inputs are Normally distributed with standard deviation below:

• StD(V) = 2
StD(d) = 0.04
StD(f) = 0.3

V

tf

dVeQ

=

Better Estimate of System Variance

22

2
2

2

2

1

)()(
2

1
)(

jii xx

n

i

n

j ji

x

n

i i

Y
σσ

xx

Y
σ

x

Y
σ  



+






=

= 

Example

Y = 25 + 200P – 2P2 + 14T

• Determine values of T & P
that minimize the STD of Y
using robustness equations &
verify with simulation

– Y = 7000

T = Normal (std = 10)

P = Normal (std = 5)

Large Scale Systems

End

Statistics homework help

Body Temperature (in degrees F)

Men Women
96.3 96.4
96.7 96.7
96.9 96.8
97 97.2
97.1 97.2
97.1 97.4
97.1 97.6
97.2 97.7
97.3 97.7
97.4 97.8
97.4 97.8
97.4 97.8
97.4 97.9
97.5 97.9
97.5 97.9
97.6 98
97.6 98
97.6 98
97.7 98
97.8 98
97.8 98.1
97.8 98.2
97.8 98.2
97.9 98.2
97.9 98.2
98 98.2
98 98.2
98 98.3
98 98.3
98 98.3
98 98.4
98.1 98.4
98.1 98.4
98.2 98.4
98.2 98.4
98.2 98.5
98.2 98.6
98.3 98.6
98.3 98.6
98.4 98.6
98.4 98.7
98.4 98.7
98.4 98.7
98.5 98.7
98.5 98.7
98.6 98.7
98.6 98.8
98.6 98.8
98.6 98.8
98.6 98.8
98.6 98.8
98.7 98.8
98.7 98.8
98.8 98.9
98.8 99
98.8 99
98.9 99.1
99 99.1
99 99.2
99 99.2
99.1 99.3
99.2 99.4
99.3 99.9
99.4 100
99.5 100.8

Statistics homework help

Chapter 13 Linear Optimization

Instructions: Please submit your work in one single Excel file with one tab/worksheet for each problem.

1. (50 points) Rosenberg Land Development (RLD) is a developer of condominium properties in the Southwest United States. RLD has recently acquired a 40.625-acre site outside Phoenix, Arizona. Zoning restrictions allow at most eight units per acre. Three types of condominiums are planned: one-, two-, and three-bedroom units. The average construction costs for each type of unit are $450,000, $600,000, and $750,000, respectively. These units will generate a net profit of 10%. The company has equity and loans totaling $180 million dollars for this project. From prior development projects, senior managers have determined that there must be a minimum of 15% one-bedroom units, 25% two-bedroom units, and 25% three-bedroom units.

a. Develop a mathematical model to determine how many of each type of unit the developer should build.

b. Implement your model on a spreadsheet and find an optimal solution.

2. (50 points) Kelly Foods has two plants and ships canned vegetables to customers in four cities. The cost of shipping one case from a plant to a customer is given in the following table.

Plant\Customer

Chicago

Cincinnati

Indianapolis

Pittsburgh

Akron

$1.70

$2.30

$2.50

$2.15

Evansville

$1.95

$2.35

$1.65

$2.95

The plant in Akron has a capacity of 3,500 cases per week, and the Evansville plant can produce 4,000 cases per week. Customer orders for the next week are as follows:

Chicago: 1,200 cases

Cincinnati: 2,000 cases

Indianapolis: 2,500 cases

Pittsburgh: 1,400 cases

Find the minimum cost shipping plan.

Statistics homework help

Chapter 13 Linear Optimization

Instructions: Please submit your work in one single Excel file with one tab/worksheet for each problem.

1. (50 points) Rosenberg Land Development (RLD) is a developer of condominium properties in the Southwest United States. RLD has recently acquired a 40.625-acre site outside Phoenix, Arizona. Zoning restrictions allow at most eight units per acre. Three types of condominiums are planned: one-, two-, and three-bedroom units. The average construction costs for each type of unit are $450,000, $600,000, and $750,000, respectively. These units will generate a net profit of 10%. The company has equity and loans totaling $180 million dollars for this project. From prior development projects, senior managers have determined that there must be a minimum of 15% one-bedroom units, 25% two-bedroom units, and 25% three-bedroom units.

a. Develop a mathematical model to determine how many of each type of unit the developer should build.

b. Implement your model on a spreadsheet and find an optimal solution.

2. (50 points) Kelly Foods has two plants and ships canned vegetables to customers in four cities. The cost of shipping one case from a plant to a customer is given in the following table.

Plant\Customer

Chicago

Cincinnati

Indianapolis

Pittsburgh

Akron

$1.70

$2.30

$2.50

$2.15

Evansville

$1.95

$2.35

$1.65

$2.95

The plant in Akron has a capacity of 3,500 cases per week, and the Evansville plant can produce 4,000 cases per week. Customer orders for the next week are as follows:

Chicago: 1,200 cases

Cincinnati: 2,000 cases

Indianapolis: 2,500 cases

Pittsburgh: 1,400 cases

Find the minimum cost shipping plan.

Statistics homework help

Regression

Simple Linear Least Squares Regression

Simple linear regression is used to estimate the coefficients of the model

i i i
y a bx e= + + (14.1)

where y
i
is the dependent variable,

xi is the independent variable, and

ei is the residual; the error in the fit of the model.

Simple Linear Least Squares Regression

28 30 32 34 36 38 40 42 44
110

120

130

140

150

160

Independent Variable

D
e
p

e
n

d
e
n

t
V

a
ri

a
b

le

Multiple Regression

0 1 1 2 2

i i i k ki i
y b b x b x b x e= + + + + +

where yi is the dependent variable,

x1i, x2i,…, xki, are the independent variables, and

ei is the residual; the error in the fit of the model.

Regression Assumptions

• Linearity of the relationship between dependent and
independent variables

• Constant variance of the errors

• Independent predictors

• Independence of the dependent values over time

• Normality of the error distribution

Linearity of the Relationship Between
Dependent and Independent Variables

• Nonlinear relationship
• Problems

• Significant predictors have non-significant p-value

• Prediction and confidence limits incorrect

• What to do
• Always plot each predictor individually and perform a visual check

• Transform data using the appropriate non-linear model

• Interactions
• Problems

• The interaction adds to the statistical noise

• A larger sample size is needed to detect statistically significant main effects

• Significant factors may be missed if the interaction has a large effect

• What to do
• Do not use the mean square as an estimate for noise in the system

• Do not use the standard error of the coefficient as an estimate for noise in the system

• A pattern can be detected on individual scatter plots

Nonlinear Relationship

Nonlinear Relationship

50403020100

600

500

400

300

200

100

0

x1

y
S 175.244

R-Sq 0.6%

R-Sq(adj) 0.0%

Fitted Line Plot
y = 217.1 – 0.999 x1

Nonlinear Relationship

• Solution
• Add x2 as a predictor

• Y = co + c1x + c2x
2 + error

Excel

1. Draw a scatter graph

2. Add a trend line

3. Select the appropriate non-linear model

Limitations

1. Only works with a single

predictor

2. Only handles 5 types of

non-linear equations

Excel Analysis Tool Pak

1. Add additional columns to model desired equation

2. Perform regression with Analysis Tool Pak
1. Tools

2. Data Analysis (May need to select using add-ins menu)

3. Regression
x x^2 y

33 1089 64.4

13 169 144.5

3 9 484.2

9 81 256.5

2 4 529.8

40 1600 225.3

7 49 324.7

Excel Analysis Tool Pak
SUMMARY OUTPUT

Regression Statistics

Multiple R 0.999999

R Square 0.999997

Adjusted R Square 0.999997

Standard Error 0.29061

Observations 48

ANOVA

df SS MS F Significance F

Regression 2 1421905 710952.5 8418177 4.0427E-126

Residual 45 3.80045 0.084454

Total 47 1421909

CoefficientsStandard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%

Intercept 625.6399 0.13127 4766.067 5.7E-130 625.3754741 625.9042553 625.3754741 625.9042553

x -50.00772 0.012358 -4046.525 0% -50.03260973 -49.9828284 -50.03260973 -49.9828284

x^2 1.000023 0.000245 4089.723 0% 0.999530235 1.000515216 0.999530235 1.000515216

-1

0

1

0 10 20 30 40 50 60

Limitations

1. You must transform data

Also gives all statistical graphs

Nonlinear Relationship Multiple predictors

210-1-2

99

90

50

10

1

Residual

P
e

r
c
e

n
t

4035302520

2

1

0

-1

Fitted Value

R
e

s
id

u
a

l

2.01.61.20.80.40.0-0.4-0.8

16

12

8

4

0

Residual

F
r
e

q
u

e
n

c
y

4035302520151051

2

1

0

-1

Observation Order

R
e

s
id

u
a

l

Normal Probability Plot Versus Fits

Histogram Versus Order

Residual Plots for T (Kelvin)

Nonlinear Relationship Multiple predictors

3.02.62.2 3.02.52.0 3.02.52.0

40

30

20

3.02.52.0

40

30

20

3.02.52.0 3.02.52.0

P (A tm)

T
(

K
e

lv
in

)

V (Liter) n (Moles)

x1 x2 x3

Scatterplot of T (Kelvin) vs P (Atm), V (Liter), n (Moles), x1, x2, x3

Source of

non-linearity

may not be

obvious

Nonlinear Relationship Multiple predictors

Nonlinear Relationship Multiple predictors

• The regression correctly identified the predictors

• How good is the equation?
• Maximum temperature =44.5
• Minimum temperature = 19.95
• The maximum residual is 1.86
• The worst error is 6.1% of the temperature range

• Use you engineering judgment
• Is 6.1% error OK?
• The error is worse when low and high temperatures are predicted

• What if we extrapolate?
• We are doomed!

P (Atm) 4

V (Liter) 4

n (Moles) 2

Predicted T (K) 75.94

True T (K) 97.49

Nonlinear Relationship Interactions

•Y = B + E – 5BE

A B C D E F Output

-1 -1 -1 1 1 1 5.14

1 -1 -1 -1 -1 1 -6.92

-1 1 -1 -1 1 -1 -2.89

1 1 -1 1 -1 -1 5.26

-1 -1 1 1 -1 -1 -6.73

1 -1 1 -1 1 -1 5.15

-1 1 1 -1 -1 1 5.30

1 1 1 1 1 1 -2.55

1 1 1 1 1 1 -2.76

Nonlinear Relationship Interactions

The interaction is treated as experimental error

This increase in error masks the effect of the coefficients

Neither B or E appear as statistically significant

Nonlinear Relationship Interactions

•Without Interaction

Experimental error (SE Coef) is much lower

B and E are statistically significant

Nonlinear Relationship Interactions

•Y = B + E – 5BE
A B C D E F Output

0.480 -0.159 -0.326 -0.397 -0.531 -0.647 -0.650

-0.162 -0.174 0.796 0.084 0.954 -0.528 1.670

-0.016 -0.319 -0.224 0.120 0.074 0.794 -0.002

0.604 -0.032 0.260 -0.227 0.302 0.855 0.704

-0.053 -0.560 0.428 -0.965 0.999 -0.161 3.640

-0.712 0.560 -0.043 -0.021 0.160 0.949 0.681

-0.431 -0.308 0.862 -0.527 -0.352 -0.088 -0.806

-0.985 -0.973 -0.866 -0.747 -0.489 0.983 -3.728

0.173 0.585 -0.424 0.353 0.173 0.173 0.353

0.778 -0.219 -0.788 -0.293 -0.119 0.227 -0.437

0.009 0.984 0.348 0.141 0.707 -0.197 -1.453

-0.101 -0.197 -0.874 -0.335 -0.592 -0.653 -1.252

-0.734 0.861 0.079 -0.487 0.727 -0.776 -1.358

-0.797 0.219 0.125 0.480 -0.852 0.769 0.323

-0.843 -0.121 -0.949 0.970 0.646 0.677 1.256

0.763 0.965 -0.209 0.198 -0.865 0.783 4.629

All data is not shown

There are 50 rows of data

Nonlinear Relationship Interactions

Both B and E are

statistically significant

Nonlinear Relationship Interactions

10-1 10-1 10-1

5.0

2.5

0.0

-2.5

-5.0

10-1

5.0

2.5

0.0

-2.5

-5.0

10-1 10-1

A

O
u

t
p

u
t

B C

D E F

Scatterplot of Output vs A, B, C, D, E, FPattern

Indicates

Significance

Pattern

Indicates

Significance

Linearity of the Relationship Between
Dependent and Independent Variables

• Nonlinear relationship
• Problems

• Significant predictors have non-significant p-value

• Prediction and confidence limits incorrect

• What to do

• Plot each predictor individually and perform a visual check

• Transform data using the appropriate non-linear model

• Interactions
• Problems

• The interactions may add to the statistical noise

• A larger sample size is needed to detect statistically significant main effects

• Significant factors may be missed if the interaction has a large effect

• What to do

• Add interactions manually if there are enough degrees of freedom

• Do not use the mean square as an estimate for noise in the system

• Do not use the standard error of the coefficient as an estimate for noise in the system

• A pattern can be detected on individual scatter plots

Constant Variance of the Errors

• Problems
• Confidence limits not valid

• Prediction limits not valid

• What to do
• Nothing is required unless prediction or confidence limits are needed

• Perform regression on subsets of the data
• Example; original data 20 < x < 100

• Make 4 data sets
20 < x < 40
40 < x < 60
60 < x < 80
80 < x < 10

Constant Variance of the Errors

500400300200100

8

6

4

2

0

-2

-4

-6

-8

Fitted Value

R
e

s
id

u
a

l

Versus Fits
(response is Y)

Constant Variance of the Errors

•Confidence limits and Prediction limits are not valid

200150100500

700

600

500

400

300

200

100

0

x

Y

S 34.6383

R-Sq 94.5%

R-Sq(adj) 94.3%

Regression

95% PI

Fitted Line Plot
Y = 106.0 + 2.418 x

Constant Variance of the Errors

•P-values are approximately correct

Independent Predictors
• What happens if the predictors are not independent?

• What causes predictors to be dependent?
• Stiffness is increased when diameter is reduced

• Coolant density is increased when cutting speed in increased

• Example
x1 x2 x3 x4 x5 y

23.2 47.2 27.4 0.6 70.9 95.1

11.5 49.8 26.3 7.5 61.3 107.5

3.5 22.6 39.5 27.3 26.9 73

17.1 5.3 8.7 17.5 22.9 28.7

4.9 5.5 14.3 13.5 11.3 24.6

24.7 7.7 48.5 1.7 32.4 17.7

41.1 12.2 13 39.9 53.9 64.8

38.3 19.7 43.3 19 58.1 59.3

4.4 33.1 1 8.8 38.2 75.9

41.3 25.8 36.9 8.6 67.1 60.3

5.8 20.2 11.4 21.2 26.9 62.2

All data is not shown

There are 48 rows of data

9/23/2021 © SKF Group Slide 29

Independent Predictors

X2 and X4
are Significant

9/23/2021 © SKF Group Slide 30

Independent Predictors
• Let’s remove X2 as a predictor and perform regression

again

• What predictors will be significant?

X1, X4 and X5
are Significant

9/23/2021 © SKF Group Slide 31

Independent Predictors

• Why didn’t X1 and X5 appear as significant in the initial
regression?

• X5 is a function of X1 and X2
• Fix

• Never perform regression without verifying the independence of predictors
• Correlation

Independent Predictors

Options
Remove X5 or

Remove X1 and X2

Independence of the Dependent
Values Over Time

• This is detected in the residuals versus order chart

• It is also detected in the normal probability chart

• Causes
• Data is correlated to itself

• Manufacturing
• Change tool, process degrades, then tool is changed again

• Mold heats up over time

• Engineering
• Technician learns & improves

• Technician get fatigued and get worse

• First part gets cold tools

Independence of the Dependent
Values Over Time

20100-10-20

99.9

99

90

50

10

1

0.1

Residual

P
e

r
c
e

n
t

20-2-4

20

10

0

-10

-20

Fitted Value

R
e

s
id

u
a

l
181260-6-12

20

15

10

5

0

Residual

F
r
e

q
u

e
n

c
y

15
0

14
0

13
0

12
0

11
0

10
09080706050403020101

20

10

0

-10

-20

Observation Order

R
e

s
id

u
a

l

Normal Probability Plot Versus Fits

Histogram Versus Order

Residual Plots for y

Classic Pattern for

Correlated Ys

The variation in a

Short time period

is much smaller

than the total

variation

Independence of the Dependent
Values Over Time

• Problems
• All statistics are unreliable because

• P-value

• Coefficients

• Confidence limits

• Prediction limits

• Fix
• Use autocorrelation analysis to determine lag, or

• Remove autocorrelation and model residuals, or

• Correct the underlying problem in the manufacturing or engineering process

Independence of the Dependent
Values Over Time

•Use every 11th

data point

35302520151051

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

Lag

A
u

t
o

c
o

r
r
e

la
t
io

n

Autocorrelation Function for y
(with 5% significance limits for the autocorrelations)

Normality of the Error Distribution

1050-5

99.9

99

90

50

10

1

0.1

Residual

P
e

r
c
e

n
t

240180120600

12

9

6

3

0

Fitted Value

R
e

s
id

u
a

l

1086420-2

48

36

24

12

0

Residual

F
r
e

q
u

e
n

c
y

1
50

1
40

1
30

1
20

1
10

1
009080706050403020101

12

9

6

3

0

Observation Order

R
e

s
id

u
a

l

Normal Probability Plot Versus Fits

Histogram Versus Order

Residual Plots for y

Normality of the Error Distribution

• Problems
• The prediction limits will not be correct

• The confidence intervals will have some error

• Fix
• There is no fix

• Why it happens
• This is unusual

• The regression is fit by minimizing the sum of the squared residual values

• Non normal data commonly produces normally distributed residuals

• Can be caused by an unknown predictor

9/23/2021 © SKF Group Slide 39

Summary

• When performing regression
• Check for correlated predictors

• Check residual graph for patterns

• Check time series graph for patterns

• Violating assumptions does not make analysis totally
invalid

• Coefficients may be OK

• P-values may be OK

Modified Power Example

x y
0.00001 -132.575
0.0002 -117.1
0.0004 -107.875
0.0006 -105.075
0.0008 -101.35
0.001 -106.65
0.002 -67.225
0.005 -27.5
0.01 -4.1