ANOVA is a hypothesis testing technique used to compare the equality of means for two or more groups; for example, it can be used to test that the mean number of computer chips produced by a company on each of the day, evening, and night shifts is the same. Give an example of an application of ANOVA in an industrial, operations, or manufacturing setting that is different from the examples provided in the overview. Discuss and share this information with your classmates. In responding to your peers, select responses that use an ANOVA application that is different from your own. Are the results of the ANOVA application statistically significant? Why are the results significant or not significant? Explain your reasoning. Consider how ANOVA could be applied to the final project case study. Support your initial posts and response posts with scholarly sources cited in APA style. https://statistics4beginners.wordpress.com/2015/02/18/how-to-calculate-anova-in-excel-2013/ PLEASE GIVE A 1-2 PARAGRAPH RESPONSE TO THE FOLLOWING: 1. In this module, our goal is to learn the statistical process of comparing several population means through a procedure called "analysis of variance", or ANOVA. ANOVA uses the variance from the mean of 2 or more sample populations to see if there is a statistically significant difference between them (Sharpe, DeVeaux, Velleman, 2016). We've learned that this is a valuable tool in all sorts of areas of study, including automotive, chemical, and medical industries. There are many practical examples of ANOVA throughout business. As previously mentioned, the medical field can benefit from the use of this statistics tool. For example, a drug company may be interested in the results of clinical trials for a few new drugs they plan to release. Medicine A, B, and C are all now in the clinical testing phase, so the instances in which each cures a specific ailment can be summed up using ANOVA. Each of the individual drugs, through the course of multiple trials, will have a number of "cured" patients. The following is an example of what the results may be, in table format:                                      A                              B                                 C Trial                1             4                              9                                  2                        2             5                              8                                  7                        3             7                              1                                  6                        4             6                              1                                  5                        5             6                              4                                  9        Using ANOVA to evaluate the variance from the mean for each trial, the ultimate goal would be to compare each trial to one another. By comparing the variance, we can say, with statistical confidence, that one medicine may be more effect.

1. ANOVA is a hypothesis testing technique used to compare the
equality of means for two or more groups; for example, it can
be used to test that the mean number of computer chips
produced by a company on each of the day, evening, and night
shifts is the same. Give an example of an application of
ANOVA in an industrial, operations, or manufacturing setting
that is different from the examples provided in the overview.
Discuss and share this information with your classmates.
In responding to your peers, select responses that use an
ANOVA application that is different from your own. Are the
results of the ANOVA application statistically significant? Why
are the results significant or not significant? Explain your
reasoning. Consider how ANOVA could be applied to the final
project case study.
Support your initial posts and response posts with scholarly
sources cited in APA style.
https://statistics4beginners.wordpress.com/2015/02/18/how-to-
calculate-anova-in-excel-2013/
PLEASE GIVE A 1-2 PARAGRAPH RESPONSE TO THE
FOLLOWING:
1.
In this module, our goal is to learn the statistical process of
comparing several population means through a procedure called
"analysis of variance", or ANOVA. ANOVA uses the variance
from the mean of 2 or more sample populations to see if there is
a statistically significant difference between them (Sharpe,
DeVeaux, Velleman, 2016). We've learned that this is a
valuable tool in all sorts of areas of study, including
automotive, chemical, and medical industries.

2. There are many practical examples of ANOVA throughout
business. As previously mentioned, the medical field can
benefit from the use of this statistics tool. For example, a drug
company may be interested in the results of clinical trials for a
few new drugs they plan to release. Medicine A, B, and C are
all now in the clinical testing phase, so the instances in which
each cures a specific ailment can be summed up using ANOVA.
Each of the individual drugs, through the course of multiple
trials, will have a number of "cured" patients. The following is
an example of what the results may be, in table format:
A B
C
Trial 1 4 9
2
2 5 8
7
3 7 1
6
4 6 1
5
5 6 4
9
Using ANOVA to evaluate the variance from the mean for each
trial, the ultimate goal would be to compare each trial to one
another. By comparing the variance, we can say, with statistical
confidence, that one medicine may be more effective than the
other two. This sort of analysis would help the company decide
which of the medicines to push to the consumer markets.
Citations
Sharpe, N. D., DeVeaux, R. D., & Velleman, P. (2016).
Business Statistics (Third ed.). Retrieved from

3. https://view.ebookplus.pearsoncmg.com/ebook
2.
Going back to my module 3 and module 5 discussion post
examples, I work within the IT department of a large company.
We are forming new software development teams using agile
development practices. We want to better understand if the
make-up of the team has any impact to the number of defects
that are produced per 1000 lines of code. We want to see If the
mean number of defects per 1000 lines of code is different for a
development team with a senior developer and a senior tester,
one with a junior developer and a senior tester, one with a
senior developer and a junior tester, and one with both a junior
developer and junior tester.
In order to determine if the mean number of bugs found per
1000 lines of code is different for these four types of teams, we
would use ANOVA analysis and use a sampling of the last 15
projects that each type of team has worked on and we gather the
number of defects per 1000 lines of codes for each of these
projects. Our hypothesis is that of the four project team types at
least one of the means of bugs per 1000 lines of code is
different from the other teams. The first step would be to create
a box plot of the results of the four teams’ bugs per 1000 lines
of code. Next, we can perform an ANOVA analysis on the
results using a 5% significance level. If we find that the p-value
is smaller than the significance level, we can reject the null
hypothesis that means of the four teams are the same.
Additionally, per Statistics For Beginners (2015), "if the F > F
crit, we reject the null hypothesis. The means of
the…populations are not equal."

4. References:
Statistics For Beginners. (2015, February 18). How To
Calculate ANOVA (ONE WAY ANOVA) IN EXCEL 2013.
Retrieved
from https://statistics4beginners.wordpress.com/2015/02/18/ho
w-to-calculate-anova-in-excel-2013/
QSO 510 Scenario Analysis Guidelines and Rubric
Knowledge of statistics is important foundational knowledge for
analyzing data. Equally important is what you can do with that
information. An overarching goal
of this course is to consider how statistics informs decision
making, or data-based decision making. Throughout this course,
you will be asked to make decisions
and then to consider the impact of those choices. Whether in
stock trading, in car sales, or on the production floor, the
decisions you make as a business
professional should be directly influenced by the data available
to you. Careful analysis is the key to data-based decision
making.
Each module task below provides a scenario and a list of
questions for you to answer using data-based decision making.

5. Specifically, the following critical elements must be addressed:
I. Main Elements
II. Integration and Application
III. Analysis
IV. Critical Thinking
Guidelines for Submission: Your analysis of the scenario must
be submitted as a 1- to 2-page Microsoft Word document with
double spacing and 12-point Times
New Roman font.
Instructor Feedback: This activity uses an integrated rubric in
Blackboard. Students can view instructor feedback in the Grade
Center. For more information,
review these instructions.
http://snhu-
media.snhu.edu/files/production_documentation/formatting/rubr
ic_feedback_instructions_student.pdf

6. Rubric
Critical Elements Exemplary (100%) Proficient (90%) Needs
Improvement (70%) Not Evident (0%) Value
Main Elements Thoroughly addresses each of the
main elements found in the
individual prompts and guiding
questions for each scenario
Adequately addresses all of the
main elements found in the
individual prompts and guiding
questions for each scenario
Addresses most but not all of the
main elements found in the
individual prompts and guiding
questions for scenario
Addresses less than half of the
main elements found in the
individual prompts or guiding
questions for each scenario
20
Integration and
Application
All of the course concepts are
correctly applied
Most of the course concepts are
correctly applied

7. Some of the course concepts are
correctly applied
Does not correctly apply any of
the course concepts
20
Analysis Meets “Proficient” and the
quality of the statistical analysis
is above minimum quality
standards for competent
Represents competency with
respect to the statistical analysis
Statistical analysis is evident, but
does not meet standards
Statistical analysis is not evident 40
Critical Thinking Draws insightful conclusions that
are thoroughly defended with
peer-reviewed evidence and
examples
Draws informed conclusions that
are justified with evidence based
on peer-reviewed research
Draws logical conclusions, but
does not defend with evidence
based on peer-reviewed research
Does not draw logical conclusions 10

8. Articulation of
Response
Submission is free of errors
related to citations, grammar,
spelling, syntax, and organization
and is presented in a professional
and easy to read format
Submission has no major errors
related to citations, grammar,
spelling, syntax, or organization
Submission has major errors
related to citations, grammar,
spelling, syntax, or organization
that negatively impact readability
and articulation of main ideas
Submission has critical errors
related to citations, grammar,
spelling, syntax, or organization
that prevent understanding of
ideas
10
Earned Total 100%

9. QSO 510 Module Ten 1
Module Nine explored sources of process variation and the use
of control charts to eliminate
unusual sources of variation to ensure that an operations process
is “on control.” Module
Ten introduces decision making under uncertainty and risk
along with payoff tables and
decision trees as vehicles to facilitate decision making.
In making decisions, one considers alternative courses of
action, states of nature that are
naturally occurring events not controlled by the decision maker,
and the potential payoffs
(usually monetary rewards, sometimes costs) from each course
of action. For example, a
new college graduate may consider two alternative courses of
action: a job offer in Houston,
Texas, and a job offer in New York City. She may encounter
two states of nature: a low cost
of living (COL) and a high cost of living. The payoffs, the
monetary values of the job offers in
each city considering the COL, are shown in the payoff table
below.
States of Nature
Actions Low COL High COL
Job Offer Houston $80,000 95,000
Job Offer New York
City

10. 74,000 140,000
The decision maker may face conditions of uncertainty or risk
in making her decision. Under
uncertainty, insufficient information exists to assign
probabilities to the state of nature. A
decision is made based on the decision maker’s optimism or
pessimism about the cost of
living. The pessimist will use the maximin strategy to make a
decision. The optimist will
make a decision using the maximax strategy.
Using the maximax strategy, the maximum payoff from each
alternative course of action is
chosen and the maximum of those maximums is selected. Based
on the table above, the
maximum payoff from the Houston job offer is $95,000 and the
maximum payoff from the
New York City offer is $140,000. The maximum of those two
payoffs is $140,000. The
decision maker should select New York City with a potential
payoff of $140,000.
Using the maximin strategy of the pessimist, the minimum
payoff from each alternative
course of action is chosen and the maximum of those minimums
is selected. Using the table
above, the minimum payoff from the Houston job offer is
$80,000 and the minimum payoff
from the New York City offer is $74.000. The maximum of
those two payoffs is $80,000. The
decision maker should select Houston with a potential payoff of
$80,000.

11. 2 QSO 510 Module Ten
Under risk, either historical probabilities or subjective
probabilities can be assigned to the
state of nature. Using the prior year’s COL published indices,
the probability of a low COL is
0.4 and the probability of a high COL is 0.6. Using the expected
value (EV) criterion and
applying these probabilities provides the following results:
EV(Houston) = 0.4(80,000) + 0.6(95,000) = $89,000
EV(NYC) = 0.4(74,000) + 0.6(140,000) = $113,600
The decision maker should select the New York City offer with
an expected value of
$113,600.
Consider some additional examples of decision making. An oil
pump manufacturer has to
make a decision to purchase pistons used in the pumps or
manufacture them in the
company’s machine shop. The decision will be made given two
states of nature, sales are
low or sales are high for the oil pumps with potential profits
from each option. A sales
manager who travels to a nearby city for business must decide
to travel by train or by plane.
The final decision considers the cost of each option and two
states of nature, inclement

12. weather or good weather on that day.
QSO 510 Module Eight 1
Module Seven compared several population means through a
statistical procedure called
analysis of variance (ANOVA). Module Eight introduces
contingency tables to summarize
categorical data and a chi-square test for the independence of
two categorical sets of data.
The previous modules of this course considered data that is
quantitative and measurable.
This module examines count data that falls into categories, or
classes. Count data can be
summarized with the use of contingency tables. A contingency
table displays counts for two
variables measured on a nominal level of measurement. You
may recall that nominal data is
count data with no natural order to the categories. For example,
a business school dean
may categorize accounting graduates by gender and whether or
not they have passed the
certified public accountant (CPA) examinations. That data is
summarized in the following
contingency table:
Gender Passed CPA
Exam

13. Did Not Pass CPA
Exam
Total
Male 7 3 10
Female 12 2 14
Total 19 5 24
Related to contingency tables is the chi-square test of
independence for two categorical
variables. Consider the following examples:
operates two shifts, a day
shift and an evening shift. A chi-square may be used to verify
that productivity of
fertilizer is independent of the shift on which it was
manufactured.
their satisfaction with
the benefits offered by the company. Employees surveyed are
paid hourly or salaried
and their satisfaction is categorized as satisfied, neutral, or
dissatisfied. The manager

14. may use a chi-square test to verify that employee satisfaction
with the benefits offered
is independent of the type of pay for these employees.
concerned about the use of
cell phones in motor vehicles and its effect on the number of
accidents in the city. A
chi-square test may show that cell phone use in a vehicle is
independent or has no
effect on the accident rate in that city.
turer of athletic shoes receives materials required
to make the shoes from
four suppliers. Athletic shoes are categorized as acceptable or
unacceptable. The
2 QSO 510 Module Eight
company’s quality control manager may use a chi-square test to
determine whether
the acceptability of the athletic shoes is related to the supplier
of the component
materials.

15. Hypotheses that accompany a chi-square test of independence
include a null hypothesis of
independence between two categorical variables and an
alternative hypothesis that a
relationship exists between the two categorical variables. As
Module Eight will show, the chi-
square test is useful for establishing the independence of two
variables that cannot be
quantified and measured, nor analyzed by the traditional
correlation coefficient.
QSO 510 Module Seven 1
Module Six introduced hypotheses and hypothesis testing on a
single population mean.
Module Seven compares several population means through a
statistical procedure called
analysis of variance (ANOVA). One-way ANOVA, also referred
to as one-factor ANOVA or
completely randomized design, is a part of Design of
Experiments, a larger subset of
statistics used extensively in the automotive, chemical, and
medicinal drug industries.
How does the ANOVA test work? To determine whether the
various sample means came
from a single population or populations with different means,
you actually compare these
sample means through their variances. For example, a general

16. manager of a chemical plant
may wish to determine whether a difference exists in the annual
salaries of his shift
supervisors, assistant plant managers, and maintenance
managers. Within-group variation
exists among salaries in each of the three groups, and between-
group variation is present
across the three groups. ANOVA uses a ratio of between-group
variation to within-group
variation to form an F statistic. If the F statistic results in a p
value that is less than or equal
to a given significance level (typically 5%), then he may
conclude that the salaries of shift
supervisors, assistant plant managers, and maintenance
managers are significantly
different. If the p value exceeds the significance level, then the
annual salaries of the three
groups are not significantly different.
Note that probability computation for an F statistic is based on
an F distribution. There is not
a single F distribution but a family of F distributions. A
particular member of the family is
determined by two parameters: the degrees of freedom in the
numerator and the degrees of
freedom in the denominator.
Consider another example of ANOVA. A professor taught four
small sections of Quantitative
Analysis last semester, which resulted in the following data on
student scores by section:
Section 1 Section 2 Section 3 Section 4
94 75 70 68

17. 90 68 73 70
85 77 76 72
80 83 78 65
88 80 74
68 65
65
2 QSO 510 Module Seven
The professor would like to know whether there is a difference
in the mean scores for
students in the four sections. Using statistical software to
analyze the data with ANOVA
provides the following results:
ANOVA
Source of
Variation SS df MS F P value F crit
Between
Groups 440.4933 3 146.8311 2.530122 0.089662 3.159908
Within
Groups 1044.598 18 58.0332

18. Total 1485.091 21
Note that F = 2.53 and p = 0.089662. At a significance level of
0.05, H0 will not be rejected
and we conclude that the mean scores of students in the four
sections of the course are not
significantly different.
Additional applications of ANOVA may include a researcher
using ANOVA to test for a
difference in the effectiveness of three drugs in treating
Alzheimer’s disease. Or, an
automotive engineer may use ANOVA to test for a difference in
three fuel blends on the
performance of the company’s new engine. An operations
manager may use ANOVA to test
for a difference in delivery times for the company’s products
over four routes.
8-2 Scenario Analysis: Promotion
You volunteer some of your spare time to your local fire
department and have been asked by an assistant chief to analyze
data on firefighters who applied for promotion. The assistant
chief wants to ensure that gender bias is not a concern in the
promotion of firefighters. Shown below is data for 50
firefighters who applied for promotion and the results of a chi-
square analysis of the data.
Male
Female

19. Promoted
13
22
Not Promoted
10
5
Chi-Square Statistic
3.6845
P value
0.054919
1 What factors should the assistant chief consider in
determining the presence of gender bias in firefighter
promotion?
2 Is the promotional status of recently promoted firefighters
independent of their gender?
3 What reasons should the assistant chief convey to the fire
chief to justify the absence of gender bias in the most recent
class of firefighters who were promoted?
4 How might the presence of gender bias in promotions impact
the fire department?
For additional details, please refer to the Scenario Analysis
Guidelines and Rubric document in the Assignment Guidelines
and Rubrics section of the course.
http://researchbasics.education.uconn.edu/anova_regression_and
_chi-square/
10-2 Scenario Analysis: Printing Equipment
The owner of a small printing company is considering the
purchase of additional printing equipment to expand her
business. If the owner expands the business and sales are high,
projected profits (minus the cost of the equipment) should be
$90,000; if sales are low, projected profits should be $40,000. If
the equipment is not purchased, projected profits should be

20. $70,000 if sales are high and $50,000 if sales are low.
1. Are there options other than the purchase of additional
equipment that should be considered in making the decision to
expand the business?
2. If the owner is optimistic about the company’s future sales,
should the company expand by purchasing the equipment?
3. Is the owner’s optimism or pessimism about sales the only
factor that may impact the company’s profits?
4. The equipment to be purchased is known in the industry to
have a useful life of five years. How might this impact the
printing company?
For additional details, please refer to the Scenario Analysis
Guidelines and Rubric document in the Assignment Guidelines
and Rubrics section of the course.
http://www.public.asu.edu/~kirkwood/DAStuff/decisiontrees/ind
ex.html
https://web.archive.org/web/20140808023036/http://www.pm-
primer.com/decision-tree-risk-analysis/
https://www.mindtools.com/dectree.html
1-2-page double space Time New Roman Font. APA citation.