A School Principal Was Interested in Whether Students in the Chess

A school principal was interested in whether students in the chess club scored above or below the mean grade point average (GPA)at her school. She figured the average GPA at the school to be 2.55 with a standard deviation of .5 and noted that the distribution was approximately normal. She then figured the average GPA for 15 students in the chess club. Their mean GPA was 2.76. Did this group represent a population different from students in general at this school? (Use the .05 significance level.)
a. Use the five steps of hypothesis testing.
b. Figure the confidence limits for the 95% confidence interval.
c. Explain the logic of what you did to a person who is unfamiliar with hypothesis testing involving a sample of more than one individual. (Be sure your explanation includes a discussion of the distribution of means-what it is, the logic of how it is figured, and its role in the overall hypothesis-testing process-and the logic and computation of confidence intervals.)