13.57 Example 11.3 (p. 418) presented data from a study in which sedentary men were randomly assigned to be placed on a diet or exercise for a year to lose weight. Forty-two men were placed on a diet, while the remaining 47 were put on an exercise routine. The group on a diet lost an average of 7.2 kg, with a standard deviation of 3.7 kg. The men who exercised lost an average of 4.0 kg, with a standard deviation of 3.9 kg.

a. State and test appropriate null and alternative hypotheses to determine whether the mean weight loss would be different under the two routines for the population of men similar to those in this study. Specify the value of a that you chose to use.

b. Explain how you decided to do a pooled or unpooled test in part (a).