Doing Time. The Federal Bureau of Prisons publishes data in Prison Statistics on the times served by prisoners released from federal institutions for the first time. Independent random samples of released prisoners in the fraud and firearms offense categories yielded the following information on time served, in months.

Fraud Firearms 3.6 17.9 25.5 23.8 5.3 5.9 10.4 17.9 10.7 7.0 18.421.9 8.5 13.9 19.6 13.3 11.8 16.6 20.9 16.1

a. Do the data provide sufficient evidence to conclude that the mean time served for fraud is less than that for firearms offenses? Perform a Mann–Whitney test at a significance level of 0.05.

b. The hypothesis test in part

(a) was done in Exercise 10.45 with the pooled t-test. The assumption there is that times served for both offense categories are normally distributed and have equal standard deviations. If that in fact is true, why can you use a Mann–

Whitney test to compare the means? Is the pooled t-test or the Mann–Whitney test better in this case? Explain your answers.