Question: We wish to estimate the difference between the mean scores

We wish to estimate the difference between the mean scores on a standardized test of students taught by Instructors A and B. The scores of all students taught by Instructor A have a normal distribution with a standard deviation of 15, and the scores of all students taught by Instructor B have a normal distribution with a standard deviation of 10. To estimate the difference between the two means, you decide that the same number of students from each instructorâ€™s class should be observed.
a. Assuming that the sample size is the same for each instructorâ€™s class, how large a sample should be taken from each class to estimate the difference between the mean scores of the two populations to within 5 points with 90% confidence?
b. Suppose that samples of the size computed in part a will be selected in order to test for the difference between the two population mean scores using a .05 level of significance. How large does the difference between the two samples means have to be for you to conclude that the two population means are different?
c. Explain why a paired-samples design would be inappropriate for comparing the scores of Instructor A versus Instructor B.

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