81. Two students, Miguel Melo and Cody Watson, did a study of textbook pricing. They compared prices at the campus bookstore and Amazon.com. To be fair, they included the sales tax for the local store and added shipping for Amazon. Here are the prices for a sample of 27 books.

Campus Amazon Campus Amazon 100.41 106.94 59.50 69.24 99.34 113.94 87.66 73.84 51.53 61.44 26.56 33.98 20.45 31.59 44.63 40.39 28.69 29.89 96.69 117.99 70.66 83.94 18.06 27.94 98.81 107.74 103.06 115.74 111.56 115.99 14.61 24.69 97.22 108.29 77.03 88.04 61.89 78.44 99.34 113.94 70.39 82.94 81.81 90.74 58.17 65.74 48.88 58.94 108.38 122.09 76.50 91.94 61.63 63.49

a. Determine a 95% con dence interval for the difference of population means using the t method of Section 10.3. Check the data for normality.

Even if the normality assumption is not valid here, explain why the t method (or the z method of Section 10.1) might still be appropriate.

b. Based on the 27 differences, obtain a bootstrap sample of 1000 differences of means. Check the bootstrap distribution for normality.

c. Use the standard deviation of the bootstrap distribution along with the mean and t critical value from

(a) to get a 95% con dence interval for the difference of means.

d. Use the bootstrap sample and the percentile method to obtain a 95% con dence interval for the difference of means.

e. Compare your three con dence intervals. In the light of your results for (d), does nonnormality invalidate the results of

(a) and (c)? Explain.

f. Interpret your results. Is there a substantial difference between the two ways to buy books? Assuming that the populations remain unchanged and you have just these two sources, wherewould you buy?