# Mathematics

#### Practical Application Scenario 1

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 (for example, do you know the standard deviation of that entire population)?
- What do you know about the sample of the population you took (for example, which sample statistical parameters do you have—mean, standard deviation, variance, and so on)?

Complete the following for this assignment:

- Determine the null hypothesis, via both an explanation and a math equation.
- Determine the alternative hypothesis, via both an explanation and a math equation.
- Determine whether to accept or reject the null hypothesis. You may solve the equation manually, use the Hypothesis Tester – Single Sample file provided in Resources, or use the SAS Enterprise Guide. You may also use the Hypothesis Tester multimedia piece provided in Resources to review the process for this equation.
- Determine if the p-value indicates acceptance or rejection of the null. Use alpha = .05
- 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.

#### Practical Application Scenario 2

In this practical application scenario, you have just been hired away from the Macy’s linen department buyer position by the Mall of Elbonia (MoE), as the new food court manager. Why? Rumor had it you just earned your MBA. One week ago, the MoE conducted convenience interviews in the mall’s food court. One hundred interviews were gathered. The results are summarized in the document titled MoE Interviews, provided in the Updates and Handouts section.

In examining the interview results, you find that each customer is listed in a row and each column contains data on:

- The customer’s gender. If you need this data, use the coding convention: 0 for female, 1 for male.
- How much time the customer spent in the mall.
- How much money he or she spent on food.
- The customer’s rating of the mall’s friendliness and attractiveness.

After applying the descriptive data measures, the mean is particularly telling; you believe that you can happily tell the food court owners that the average amount mall customers spend on food during a visit has increased. A 2011 study found that customers spent an average of $18.75 per visit. You realize this is a one sample test of hypothesis situation. Use the data in the MoE Interviews document and the following outlined process to be certain that your assertions are correct and that the average amount mall customers spend on food during a visit to your mall has increased.

- Determine the null hypothesis, via both an explanation and a math equation.
- Determine the alternative hypothesis, via both an explanation and a math equation.
- Determine whether to accept or reject the null hypothesis. You may solve the equation manually or use the Hypothesis Tester – Single Sample document provided in the Resources or by using SAS Enterprise Guide.
- Determine if the p-value indicates acceptance or rejection of the null. Use alpha = .05.
- 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 average amount a food court customer spends has increased, decreased, or remained the same, and what would happen if alpha was 0.01 or 0.1.

#### Assignment Submission

Compile both of your scenario answers into one Word file (submitted as a .docx file) and copy the Excel output (or other computer application output that you used), including any graphics, tables, and so on, into that Word document.