#### Coaching companies claim that their courses can raise the SAT scores of high school students

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# Coaching companies claim that their courses can raise the SAT scores of high school students. Of course, students who retake the SAT without paying for coaching generally 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                             x            s                         x    s                      x       s Coached    500         92                       529       97                    29      59 Uncoached           506        101    527      101                    21      52 Let's first ask if students who are coached significantly increased their scores.You could use the information given to carry out either a two-sample t test comparing Try 1 with Try 2 for coached students or a matched pairs t test using Gain. Which is the correct test? Why? A. Two-sample test, because we are given data for the two samples which is more accurate than the data only on the gain. B. Matched pairs test, because we are not interested in the difference in mean between the two groups, but the gain that each student has achieved. C. Two-sample test, because matched pairs test can be performed only if we have information on every individual. D. Matched pairs test, because we are interested in the difference in mean between the two groups - not the gain that each student has achieved. Carry out the proper test. What do you conclude? A. There is sufficient evidence that coached student achieved a better score on the second try. B. There is insufficient evidence that coached student achieved a better score on the second try. C. There is no evidence that coached student achieved a better score on the second try. Give a 98% confidence interval for the mean gain of all students who are coached. A. 22.25 to 35.75 B. 20.8 to 37.2 C. 21.5 to 36.5 D. 20 to 38

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