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

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(1 point) Coaching companies claim that their courses can raise the SAT scores of high school students. Butstudents who retake the SAT without paying for coaching also usually raise their scores. A random sample ofstudents who took the SAT twice found 427 who were coached and 2733 who were uncoached. Starting with theirverbal scores on the first and second tries, we have these summary statistics:Try 1 Try 2GainXSXSXSCoached427 500 92 529 97 29 59Uncoached 2733 506 101 527 101 21 52Estimate a 96% confidence interval for the mean gain of all students who are coached.23to35at 96% confidence.Now test the hypothesis that the score gain for coached students is greater than the score gain for uncoachedstudents. Let / be the score gain for all coached students. Let wz be the score gain for uncoached students.(a) Give the alternative hypothesis: #1 - /2>O.(b) Give the t test statistic: