Question

Coaching companies claim that their courses can raise the SAT scores of high school students. But students who retake the SAT without 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

	nn	x⎯⎯⎯x¯	ss	x⎯⎯⎯x¯	ss	x⎯⎯⎯x¯	ss
Coached	427	500	92	529	97	29	59
Uncoached	2733	506	101	527	101	21	52

Estimate a 99% confidence interval for the mean gain of all students who are coached.

______to
______at 99% confidence.

Now test the hypothesis that the score gain for coached students is greater than the score gain for uncoached students. Let μ1μ1 be the score gain for all coached students. Let μ2μ2 be the score gain for uncoached students.

(a) Give the alternative hypothesis: μ1−μ2______0.

(b) Give the tt test statistic: ______

(c) Give the appropriate critical value for α=5%:_____

Answer 1

Answer