In the Journal of Marketing, Bayus studied differences between "early replacement buyers" and "late replacement buyers." Suppose that a random sample of 800 early replacement buyers yields a mean number of dealers visited of 1 = 3.3. and that a random sample of 500 late replacement buyers yields a mean number of dealers visited of 2 = 4.5. Assuming that these samples are independent:
a. Let µ1 be the mean number of dealers visited by early replacement buyers, and let µ2 be the mean number of dealers visited by late replacement buyers. Calculate a 95 percent confidence interval for µ2 - µ1. Assume here that σ1 = .71 and σ2 - .66. Based on this interval, can we be 95 percent confident that on average late replacement buyers visit more dealers than do early replacement buyers?
b. Set uµ the null and alternative hypotheses needed to attempt to show that the mean number of dealers visited by late replacement buyers exceeds the mean number of dealers visited by early replacement buyers by more than 1.
c Test the hypotheses you set up in part b by using critical values and by setting a equal to .101 .051 .011 and .001. How much evidence is there that H0 should be rejected?
d. Find the p-value for testing the hypotheses you set up in part b. Use the p-value to test these hypotheses with a equal to .101 .051 .011 and .001. How much evidence is there that H0 should be rejected? Explain your conclusion in practical terms
e. Do you think that the results of the hypothesis tests in parts e and d have practical significance? Explain and justify your answer.