Coaching companies claim that their courses can raise the SAT scores of high school students. But students who retake the SATwithoutpaying for coaching also usually 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:

Try 1Try 2

Gain

Coached 427 500 92 529 97 29 59; uncoached 2733 506 101 527 101 21 52

Use Table C to estimate a 95% confidence interval for the mean gain of all students who are coached.

to

at 95% confidence.