Question

SmArT Academy, an SAT test prep company, claims that their program improves student scores). A simple random sample of 37 students took the SAT before taking the prep course and then again after taking the prep course. The average increase in their scores after taking the course was 40 points with a standard deviation of 120 points. What can we conclude about the SmArT Academy’s claim that the course improves scores? Use a significance level of α = 0.05 and the P-value method.

(a) What is the appropriate distribution (normal or t) to use for our calculations?

(b) State the null and alternate hypothesis. Is the alternate hypothesis left, right, or two-tailed?

Answer 1

a) This is a test for difference in means but we are not given the population standard deviation here, so we cannot use the normal distribution but, we are to use the t distribution here. Therefore t distribution is to be used here.

b) As we are testing here whether program improves student scores, therefore we are to see whether the difference in means is statistically greater than 0. Therefore this is a one tailed test, specifically on the upper side that is a right tailled test.