Question: Coaching companies claim that their courses can raise the SAT scores of high school students. Of course, students who retake the SAT without paying for coaching generally raise their scores. A random sample of students who took the SAT twice found 427 who were coached and 2733 who were uncoached. Starting with their Verbal scores on the first and second tries, we have these summary statistics:
Coaching and SAT scores What we really want to know is whether coached students improve more than uncoached students, and whether any advantage is large enough to be worth paying for. Use the information above to answer these questions:
(a) How much more do coached students gain on the average? Construct and interpret a 99% confidence interval.
(b) Does the interval in part (a) give convincing evidence that coached students gain more, on average, than uncoached students? Explain.
(c) Based on your work, what is your opinion: do you think coaching courses are worth paying for?