A School Psychologist Was Interested in Whether the 12 Students

A school psychologist was interested in whether the 12 students in the chess club had a higher or lower mean grade point average (GPA)than the other students at a school.The overall GPA at the school was 2.55 with a standard deviation of 0.5; the distribution of GPAs was approximately normal.The average GPA of students in the chess club was 2.76.Using the .05 significance level,did the chess club represent a population that was different from students in general at this school?
a.Use the five steps of hypothesis testing.
b.Sketch the distributions involved.
c.Advanced topic: Figure the confidence limits for the 95% confidence interval.
d.Explain the logic of what you did to a person who understands hypothesis testing for studies in which the sample consists of a single individual but 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.Advanced topic: Explain the logic and computation of the confidence intervals.