A private school promoted itself by advertising that its graduates had an average SAT verbal score of 550 with a standard deviation of 100. At the end of the school year, the Parent-Teacher Association (PTA) decided to see if the SAT scores for students at the school were different from the advertised average and found that the average SAT verbal score for 80 graduating seniors was 532. Using the .05 significance level, what should the PTA conclude about the school's claim?
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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