A psychology professor of a large class became curious as to whether the students who turned in tests first scored differently from the overall mean on the test. The overall mean score on the test was 75 with a standard deviation of 10; the scores were approximately normally distributed. The mean score for the first 20 students to turn in tests was 78. Using the .05 significance level, was the average test score earned by the first 20 students to turn in their tests significantly different from the overall mean?
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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