The U.S. Bureau of Prisons publishes data in Statistical Report on the times served by prisoners released from federal institutions for the first time. Independent random samples of released prisoners for four different offense categories yielded the following information on time served, in months. Offense ni x̄i si Counterfeiting 13 14.5 4.5 Drug Laws 13 18.4 3.8 Firearms 13 18.2 4.5 Fraud 13 11.5 4.7
(By-Hand) The U.S. Bureau of Prisons publishes data in Statistical Report on the times served by prisoners released from federal institutions for the first time. Independent random samples of released prisoners for four different offense categories yielded the following information on time served, in months.
|
Offense |
ni |
x̄i |
si |
|
Counterfeiting |
13 |
14.5 |
4.5 |
|
Drug Laws |
13 |
18.4 |
3.8 |
|
Firearms |
13 |
18.2 |
4.5 |
|
Fraud |
13 |
11.5 |
4.7 |
Part a:
Do the data provide sufficient evidence at the 1% significance level to conclude that a difference exists in mean time served by prisoners among the four offense groups? Show all steps of the appropriate test procedure. Be sure to list any assumptions that are assumed to be true (do not create any plots).
Part b:
Use Tukey-Kramer (Tukey’s W) to determine any differences in the mean time served by prisoners among the four offense groups (be sure to include an underline graphic and sentence), or explain why you don’t think there is a difference in the mean time served by prisoners among the four offense groups.
Part c:
Which offense group(s) do you think yield the shortest mean time served? Be sure to include information from your analysis above as the basis for your answer.
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