EXAMPLE 7 Calculating

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image Clothing Store Sales

Retail stores need to generate sales. A sample of 100 customers' data was taken from the Chapter 9 Case Study data set, Clothing Store, and the total sales were obtained for each customer during the six-month time period. Suppose this sample showed a sample mean of . Assume the population standard deviation is . The district manager has set a goal to achieve a population mean of more than $413 total sales per customer.

  1. Construct the hypotheses.
  2. Calculate the test statistic .

Solution

  1. Using our strategy for constructing the hypotheses from Section 9.1, the key words “more than” means “>,” and the “>” symbol occurs only in the right-tailed test. Answering the question “More than what?” is . Thus, our hypotheses are

    where represents the population mean total sales per customer.

  2. The sample size is , with a sample mean of , and . Thus,

NOW YOU CAN DO

Exercises 9–22.