(2 pts) Coaching companies claim that their courses can raise the SAT scores of high school students. But students who retake the SATwithout paying 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 1 Try 2 Gain
| n | x¯ | s | x¯ | s | x¯ | s | |
| 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.
Now test the hypothesis that the score gain for coached students is greater than the score gain for uncoached students. Let μ1 be the score gain for all coached students. Let μ2 be the score gain for uncoached students.
(a) Give the alternative hypothesis: μ1−μ2 0.
(b) Give the t test statistic:
(c) Give the appropriate critical value for α=5%: .
The conclusion is
A. There is sufficient evidence to support the claim that with coaching, the mean increase in scores is greater than without coaching.
B. There is not sufficient evidence to support the claim that with coaching, the mean increase in scores is greater than without coaching.
