Question: Alpha Omega fraternity claims that the average grade point of their members is 3.1. To test this claim, the admissions office selects a random sample of 49 fraternity members and finds that their average grade point is 2.9 with a standard deviation of 0.25.

a. Should the fraternity's claim be rejected at the 0.05 level of significance?

b. Find the 95% confidence interval of the mean grade point for Alpha Omega members.

c. Do the results of the hypothesis test and confidence interval concur? Explain.