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 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).