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.
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