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The Scholastic Aptitude Test (SAT) is a standardized test for college admissions in the U.S. Scores on the SAT can range from 600 to 2400. Suppose that PrepIt! is a company that offers classes to help students prepare for the SAT exam. In their ad, PrepIt! claims to produce "statistically significant" increases in SAT scores. This claim comes from a study in which 427 PrepIt! students took the SAT before and after PrepIt! classes. These students are compared to 2,733 students who took the SAT twice, without any type of formal preparation between tries. We conduct a hypothesis test and find that PrepIt! students significantly improve their SAT scores (p-value < 0.0001). Now we want to determine how much improvement we can expect in SAT scores for students who take the PrepIt! class.

Which of the following is the best approach to answering this question?

A. Use the sample mean 29 to calculate a confidence interval for a population mean.
B. Use the difference in sample means (500 − 529) in a hypothesis test for a difference in two population means (or treatment effect).
C. Use the difference in sample means (500 − 529) to calculate a confidence interval for a difference in two population means (or treatment effect).
D. Use the difference in sample means (29 and 21) in a hypothesis test for a difference in two population means (or treatment effect).

Answer :

The best approach to determine the average improvement in SAT scores for PrepIt! students is to calculate a confidence interval for the difference in two population means using the sample mean differences, option A.

To determine the average improvement in SAT scores for students who take the PrepIt! class, the best approach is to use the difference in sample means to calculate a confidence interval for a difference in two population means (or treatment effect), option A.

This involves taking the mean SAT score before the PrepIt! class and the mean SAT score after the class and computing the confidence interval for this difference. Doing this calculation will provide an interval estimate that shows the range of values within which the true mean difference in SAT scores, due to the PrepIt! class, is likely to fall. For instance, if the mean SAT score improvement is 29 points, we would use this value and the appropriate standard error and confidence level to calculate the confidence interval.

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