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 householdPlaybill?reader's income has increased, decreased, or remained the same.
- State whether you would propose that the cost of the magazine be raised.
Professors feed back:?
Identifies a null hypothesis and alternative hypothesis that are inaccurate or inappropriate for making decisions regarding household income.
Faculty Comments:?Michelle, thanks for your efforts on the hypothesis statements, but you failed to explicitly provide a correct null and research hypothesis both written and mathematically.?
Computes an inaccurate p-value to indicate acceptance or rejection of a null hypothesis regarding average household income.
Faculty Comments:?Michelle, Thanks for selecting a p-value, but without a correct hypothesis statement, you haven't provided the logic for why you selected the p-value that was chosen. Usually the p-value for this calculator is selected based on the inequality of the null hypothesis. Given that you don't have a correctly written null then the logic to support your selection is missing.?
Computes the appropriate statistical test, but incorrectly determines acceptance or rejection of a null hypothesis.
Faculty Comments:?Michelle, Thanks for your attempt at computing a statistical test. Unfortunately you selected the wrong calculator/test for this specific scenario. Additionally you didnt provide any justification for why you selected the calculator/test.?
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