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.
Question 10.90
39. What if the sample sizes for each group were some number greater than ?
- How would this affect the width of the confidence interval in Exercise 38 (b)? Is this good? Explain.
- Would this change have any effect on our conclusion in the hypothesis test in Exercise 38 (c)? Explain why or why not.
10.2.39
(a) Since the width of the confidence interval is , an increase in the sample sizes will result in a decrease in the width of the confidence interval. This is good because smaller confidence intervals give a more precise estimate. (b) It depends on how large the new sample sizes are.