Question: A cell phone company knows that the mean length of calls for all of its customers in a certain city is 9.2 minutes. The company is thinking about offering a senior discount to attract new customers, but first wants to know whether or not the mean length of calls for current customers who are seniors (65 and over) is the same as it is for the general customer pool. The only way to identify seniors is to conduct a survey and ask people whether they are over age 65. Using this method, the company contacts a random sample of 200 seniors and records the length of their last call. The sample mean and standard deviation for the 200 calls are 8 minutes and 10 minutes, respectively.
a. Do you think that the data collected on the 200 seniors are approximately bell-shaped? Explain.
b. Is it valid to conduct a one-sample t-test in this situation? Explain.
c. In spite of how you may have answered part (b), carry out the five steps to test the hypotheses of interest in this situation using a = .05. (Use a p-value, not a rejection region.)