The Cell Tone Company sells cellular phones and airtime in several northwestern states. At a recent meeting, the marketing manager stated that the average age of its customers is under 40. This came up in conjunction with a proposed advertising plan that is to be directed toward a young audience. Before actually completing the advertising plan, Cell Tone decided to randomly sample customers. Among the questions asked in the survey of 50 customers in the Jacksonville, Florida, area was the customer’s age. The data are available in a data file called Cell Phone Survey .
a. Based on the statement made by the marketing manager, formulate the appropriate null and alternative hypotheses.
b. The marketing manager must support his statement concerning average customer age in an upcoming board meeting. Using a significance level of 0.10, provide this support for the marketing manager.
c. Consider the result of the hypothesis test you conducted in part b. Which of the two types of hypothesis-test errors could you have committed? How could you discover if you had, indeed, made this error?
d. Calculate the critical value, α.
e. Determine the p -value and conduct the test using the p -value approach.
f. Note that the sample data list the customer’s age to the nearest year. (1) If we denote a randomly selected customer’s age (to the nearest year) as xi, is xi a continuous or discrete random variable? (2) Is it possible that xi has a normal distribution? Consider your answers to (1) and (2) and the fact that x must have a normal distribution to facilitate the calculation in part b. Does this mean that the calculation you have performed in part b is inappropriate? Explain your answer.