Statistics

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%.

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  1. 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.

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