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?)
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.
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.