Math SAT scores (Y) are normally distributed with amean of 1500 and a standard deviation of 140. An evening schooladvertises that it can improve students' scores by roughly a thirdof a standard deviation, or 30 points, if they attend a coursewhich runs over several weeks. (A similar claim is made forattending a verbal SAT course.) The statistician for a consumerprotection agency suspects that the courses are not effective. Sheviews the situation as follows: H0 : = 1500 vs.H1 : = 1460.
Assume that after graduating from the course, the 420participants take the SAT test and score an average of 1450. Isthis convincing evidence that the school has fallen short of itsclaim at 2.5% level?
