Assessment 3
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:
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.
Identify the null hypothesis, via both a written explanation
and a math equation.
Determine the alternative hypothesis, via both a written
explanation and a math equation.
Solve the equation to determine whether to accept or reject
the null hypothesis.
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:
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:
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.
