Ivy Bound, Inc. offers a home study program to prepare students for the college entrance exams (the SATs), suggesting that test scores will be better for those students who follow the 10 week, $ 250 home study program. To evaluate the effectiveness of the program in your area, you take a sample of 200 local students who took the home study course and 200 local students who did not. Average SAT score for the sample who took the course was 1530, with standard deviation of 56 points. The average score for the sample who did not take the course was 1480, with standard deviation of 84 points.
a. Construct and interpret the 95% confidence interval estimate of the population mean difference in scores.
b. Suppose you wanted to produce an interval estimate that had a margin of error term no larger than 0 points at the 95% confidence level. Assuming that you plan to take samples of equal size from each population (that is, n1 will be equal to n2), how large a sample from each population should you take? Use the results above as a pilot sample.