A professor was curious as to whether the students in a very large class she was teaching who turned in their 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 tests was 78. Did the students turning in their tests first score significantly different from the mean at the .05 level?
a. Use the five steps of hypothesis testing and show all work
b. Figure the confidence limits for the 95% confidence interval and 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 is it , the logic of how it is figured, and its role in the overall hypothesis testing process and the logic and computation of confidence intervals)