Essay Grade

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Solve four equations based on a scenario related to hypothesis testing. Demonstrate
your method, report your findings, and write a brief paragraph that details your
recommendations for action.
Note: The assessments in this course build upon each other, so you are strongly
encouraged to complete them in sequence.
Managers can use sampling techniques to make managerial decisions and draw
conclusions. The statistical technique that we will use to evaluate the samples is
hypothesis testing; mathematically speaking, we will use statistical techniques to
evaluate the likelihood of an assertion.
By successfully completing this assessment, you will demonstrate your proficiency
in the following course competencies and assessment criteria:
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Competency 1: Evaluate the quality and fit of data for use in business analysis.
Determine the null hypothesis and alternative hypothesis for making decisions
regarding household income.
Competency 3: Analyze business decision opportunities using basic inferential
statistics.
Compute the appropriate statistical test to determine acceptance or rejection of a
null hypothesis.
Compute the p-value to indicate acceptance or rejection of a null hypothesis
regarding average household income.
Competency 5: Apply data analysis to general business management planning and
decision making.
Compile findings into a management report with details for recommended actions.
Competency 6: Communicate in a manner that is professional and consistent with
expectations for members of the business professions.
Communicate in a manner that is professional and consistent with expectations for
members of the business professions.
Context
Managers use hypothesis testing and statistical techniques to evaluate the likelihood
of an assertion. Hypothesis testing is at the core of inferential statistics. It is the
foundation of the inferential statistics used to help managers make better decisions.
A typical managerial decision using hypothesis testing would be to compare
samples of purchased products to ensure they conform to firm quality standards. In
fact, sampling itself is a particularly useful data analysis technique. Malls and stores
often sample prospective customers. So do retail fast food franchises—take a look at
the bottom of your receipts the next time you purchase something.
Questions to Consider
To deepen your understanding, you are encouraged to consider the questions below
and discuss them with a fellow learner, a work associate, an interested friend, or a
member of the business community.
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Why is it important that a sample be random?
For its validity, all hypothesis testing depends heavily on the assumption that the
sample that is used was drawn using probability sampling techniques. Why is this
important?
What can you do if you cannot use a probability sampling technique? (For example,
suppose there is no good sampling frame available for the population of interest.)
Resources
Required Resources
The following resources are required to complete the assessment.
Capella Resources
Click the link provided to view the following resource:
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Hypothesis Tester – Single Sample.
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Suggested Resources
The resources provided here are optional. You may use other resources of your
choice to prepare for this assessment; However, you will need to ensure that they
are appropriate, credible, and valid. They provide helpful information about the
topics in this unit. The MBA-FP6018 – Data Analysis for Business Decisions Library
Guide can help direct your research. The Supplemental Resources and Research
Resources, both linked from the left navigation menu in your courseroom, provide
additional resources to help support you.
The following texts provide instruction in Statistics.
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Bowerman, B., O’Connell, R., & Murphree, E. (2014). Business statistics in practice
(7th ed.). New York, NY: McGraw Hill. Available from the bookstore
Chapter 9, “Hypothesis Testing,” in Business Statistics in Practice, pages 340–373.
The following resource is an Excel calculation tool that will assist you in completing
the assessment.
Hypothesis Tester – Single Sample.
The following resource is a tutorial for using an Excel calculation tool that will assist
you in completing the assessment.
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Hypothesis Tester | Transcript.
Additional Resources for Further Exploration
The following text provides instruction for statistical analysis in Microsoft Excel.
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Salkind, N. J. (2016). Excel statistics: A quick guide (3rd ed.). Thousand Oaks, CA:
Sage. Available from the bookstore
The following text provides instruction for SAS one of the most commonly used
statistical analysis tools in business.
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Slaughter, S. J., & Delwiche, L. D. (2010). The little SAS book for Enterprise Guide 4.2.
Cary, NC: SAS Institute. Available from the bookstore
Statistics Tutorials
Capella University partners with Sophia Learning to provide tutorials and other
learning resources online. For this assessment, you are encouraged to study the
following Sophia tutorials:
This tutorial introduces and defines the T-Statistic and its relevance to variance and
distribution within data sets.
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Fitz (Producer). (n.d.). T-statistic [Video] | Transcript. Retrieved from
http://www.sophia.org/tutorials/t-statistic–4
This tutorial illustrates a hypothesis testing procedure for a mean.
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Daunis, M. (Producer). (n.d.). Hypothesis test – Mean [Video] | Transcript. Retrieved
from http://www.sophia.org/hypothesis-test-mean-tutorial
Additional Statistics Tutorials
This website offers resources that cover many topics in statistics, including
presentations that illustrate how to use software to implement statistical methods.
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StatisticsLectures.com (Producer). (n.d.). Independent and dependent
samples [Video] | Transcript.Retrieved from
http://www.statisticslectures.com/topics/independentdependentsamples/
StatisticsLectures.com (Producer). (n.d.). Null and alternative hypotheses [Video]
| Transcript. Retrieved from http://www.statisticslectures.com/topics/hypotheses/
StatisticsLectures.com (Producer). (n.d.). One sample z-test [Video]
| Transcript. Retrieved from
http://www.statisticslectures.com/topics/onesamplez/
StatisticsLectures.com (Producer). (n.d.). One sample t-test [Video] | Transcript.
Retrieved from http://www.statisticslectures.com/topics/onesamplet/
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Assessment Instructions
Use the Hypothesis Tester – Single Sample file (linked in the Resources under
the Required Resources heading) and data analysis software to complete the
calculations for this scenario.
You may also refer to the Hypothesis Tester – An Introduction media piece (linked
in the Resources under Suggested Resources) to review the process for computing
this equation.
Practical Application Scenario
In 2010, Playbill Magazine, a regionally based magazine, consulted Boos Allen to
determine the mean annual household income of its readers. Using a list of
customers provided by Playbill, Boos Allen randomly sampled
300 Playbill customers. From that sample, Boos Allen is confident that the
average Playbill reader’s household income is $119,155, with a population sample
household income standard deviation of $30,000.
Recently, two Playbill executives suggested that the mean average household
income for Playbill readers has increased, and the magazine price should be raised.
As new marketing manager for Playbill, you convince the chief operating officer to
complete a second survey with Boos Allen to confirm that assertion. Yesterday, the
new Boos Allen report appeared on your desk. From a new sample
of Playbill customers, taken from a list of recent customers you e-mailed to Boos
Allen, the 2012 Playbill customer profile shows a mean annual household income of
$124,450, with a population standard deviation of household income unchanged at
$30,000.
You realize that you have enough data to perform a one-sample hypothesis test. In
order to choose the correct statistical tool to complete this assessment, consider the
following questions:
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What do you know about the population being studied? (For example, do you know
the standard deviation of the overall population?)
What do you know about the population sample you chose? (For example, which
sample statistical parameters do you have, such as mean, standard deviation,
variance, and so on?)
Directions
Solve the following equations, based on the data from the Hypothesis Tester –
Single Sample file. Demonstrate your method and display your results in table
format, using Excel or another appropriate computer application.
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Identify the null hypothesis, via both a written explanation and a math
equation.
4. Determine the alternative hypothesis, via both a written explanation and a math
equation.
5. Solve the equation to determine whether to accept or reject the null hypothesis.
6. Determine whether the p-value indicates acceptance or rejection of the null. Use
alpha = .05.
Next, address the following in a report to the executives:
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Write a three-sentence paragraph that details your recommendations for a course of
action, based on your results.
Report the rejection or acceptance of the null, in terms of the scenario results.
Explain why you can be statistically confident that the mean
household Playbill reader’s income has increased, decreased, or remained the same.
State whether you would propose that the cost of the magazine be raised.
Describe what would happen if alpha was .01.
Additional Requirements
Compile your work and report in a 1–2 page Microsoft Word file:
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Paste in the tables you used to make your calculations.
Clearly title your tables, including each row and column.
Highlight the results of your data calculations within each table.
Hypothesis Tester – Single Sample
Hypothesis Test for a Population Mean, Sigma Known
If the population standard deviation is known, we can directly calculate the
standard deviation of the sampling distribution (the standard error of the estimate),
and use the standardized normal distribution to get a z-multiple, using the Excel
function NORMSINV.
We can then calculate p for each of the three possible test conditions, and compare it to
each level of alpha to see whether the null hypothesis should be rejected.
Inputs:
Hypothesized population mean:
Population standard deviation (sigma):
Sample size (n):
Sample mean (x-bar):
295
12
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297,6

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