Student affairs departments at colleges provide programs and events that offer students opportunities to learn outside of traditional coursework. One popular avenue of engagement chosen by students is intramural sports. Does participation in intramural sports improve freshmen academic indicators such as GPA and retention after the first year?

This Excel fileFreshmen Intramuralshas data on 745 intramural participant/nonparticipant pairs of freshmen at a large midwestern university. The student participant/nonparticipant pairs were formed based on matching gender and high school GPA (to within 0.25).

A claim frequently made by college academic advisors is that freshmen intramural participants have higher freshman-year GPA's than freshmen who do not participate in intramurals. Let_Pbe the mean freshmen year GPA of intramuralparticipantsand_Nbe the mean freshmen year GPA of intramuralnonparticipants. Do these data support the claim that freshmen intramural participants havehigherfreshmen year mean GPA's than freshmen intramural nonparticipants? Perform the appropriate hypothesis test and answer the questions below (calculate the difference as participant freshmen year GPA - nonparticipant freshmen year GPA.

Question 1. What is the value of the test statistict? (use 2 decimal places in your answer)

Question 2. Select the correct choice below for the P-value of this hypothesis test.

0.05 < P-value < 0.10

0.001 < P-value < 0.005

0.01 < P-value < 0.05

0.005 < P-value < 0.01

P-value > 0.10

P-value < 0.0001

Question 3. What is an appropriate conclusion for this hypothesis test?

Question 4. Estimate the mean difference (freshmen year intramural participant GPA - freshmen year intramural nonparticipant GPA) in freshmen year GPA's with a95% confidence interval.