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:

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	      Try2	           Gain	
	                n	   xbar   s	   xbar	s	xbar	s
Coached	        427	  500     92  529	97	29	59
Uncoached	2733	   506  101  527	101	21	52

1)Use Table C to estimate a 99% confidence interval for the mean gain of all students who are coached.
_________to________at 99% confidence.

2) (a) Give the alternative hypothesis: μ1−μ2 > 0.

(b) Give the t test statistic: 2.6459

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

I got #2 part a and b right, but I need help finding (#1) the confidence interval and (c) the critical value for α=5%.

MathGuru · Answer

z = 2.575 for a 99% confidence. Since your sample sizes are large, I would use a two-sample confidence interval formula for large sample sizes.

Critical value at .05 using a z-table for a one-tailed test is z = 1.645

If you use a t-table instead to find critical value, then you will have to figure degrees of freedom as well.