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 96% confidence interval for the mean gain of all students who are coached.

___________ to __________ at 96% 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 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.

Answer 1

23.1181 to 34.8819 at 96% confidence.

(a) Give the alternative hypothesis: μ1 > μ2

(b) Give the t test statistic: 2.646

(c) Give the appropriate critical value for α=5%: 2.248

A. There is sufficient evidence to support the claim that with coaching, the mean increase in scores is greater than without coaching.

1	2
29	21	mean
59	52	std. dev.
427	2733	n
	534	df
	8.000	difference (1 - 2)
	3.024	standard error of difference
	0	hypothesized difference
	2.646	t
	.0042	p-value (one-tailed, upper)