The U.S. Bureau of Prisons publishes data in Statistics Report 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.
Mean s n

Sample 1: Fraud 10.12 months 4.90 35

Sample 2: Firearms 18.78 months 4.64 40

At the 5% level do the data provide sufficient evidence to conclude that the mean time served for fraud is less than that for firearms offenses? Identify the appropriate test and test the claim using the traditional method at the 0.05 level of significance.

For the problem please only answer the following:

1. Hypothesis and identify one as the claim

2. critical value(s)

3. Test Value

Katy Fit, aerobics instructor at the Anderson Recreation Center, is analyzing the attendance at her classes. She wonders if the mean number of people who come on Monday morning is the same as on Wednesday morning. Some people may be exhausted from their other weekend activities and skip Mondays. Yet others may get busy midweek and be unable to fit exercise into their schedules. Summary data for 35 randomly selected Mondays and 35 randomly selected Wednesdays are reported below. Is there a significant difference in the mean numbers of people who come to class on the two days?

a. Use the P-value method to perform the appropriate test at the 0.04 level of significance.
(Yes, I mean 0.04; it is not a typo.)

b. Find the 95% confidence interval for the difference between the two means.

Sample 1: Monday: Mean = 35 s = 9.5 n = 35

Sample 2: Wednesday: Mean = 28.5, s = 9.8 n = 35

For the problem please only answer the following:

1. Decision

2. Write a concluding statement about the claim.