Coaching for the SAT. Use this information for Exercises 37–39. The College Board reports that a pretest and post-test study was done to investigate whether coaching had a significant effect on SAT scores. The improvement from pretest to post-test was 29 points for the coached sample of students, with a standard deviation of 59 points. For the uncoached students, the pretest to post-test improvement was 21 points with a standard deviation of 52 points.
37. Suppose we consider a sample of 100 students from each group. Perform a test, at level of significance , to determine whether the population mean coached SAT pretest–post-test improvement is greater than that for the uncoached students.
10.2.37
. Reject if . . . Since the is not , we do not reject . There is insufficient evidence that the population coached SAT score improvement is greater than the population noncoached SAT score improvement. Critical-value method: . . Reject if . . Since is not , we do not reject . There is insufficient evidence at the level of significance that the population mean coached SAT improvement is greater than the population mean noncoached improvement.