In 2010, Playbill Magazine contacted Boos Allen to determine the mean annual household income of its readers.

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Question:

In 2010, Playbill Magazine contacted 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 population average Playbill reader's household income is $119,155 and has a population sample household income standard deviation of $30,000.

Recently, two Playbill executives suggested that Playbill's reader mean average household income has increased and that the magazine's price should be raised. As Playbill's new marketing manager, you convince Playbill's 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 another sample of Playbill customers taken from a recent list you sent Boos Allen, the 2012 Playbill customer's profile is a mean annual household income of $124,450 with a population standard deviation of household income unchanged at $30,000.

You realize that even though you do not have the Playbill reader population standard deviation, you do have enough data to perform a one sample hypothesis test. In order to choose the correct statistical tool to complete this assignment, consider the following questions:

What do you know about the population being studied?

What do you know about the sample of the population you took?

Requirements:

1. Determine the null hypothesis, via both an explanation and a math equation.

2. Determine the alternative hypothesis, via both an explanation and a math equation.

Report the rejection or acceptance of the null in terms of the scenario results. For this scenario, write a three-sentence paragraph that details why you can be statistically confident that the mean household Playbill reader's income has increased, decreased, or remained the same, and what would happen if alpha was .01.