(Solved): 21.32 Coaching and SAT Scores. Coaching companies claim that their courses can raise the SAT scores ...

21.32 Coaching and SAT Scores. 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, too. A random sample of students who took the SAT twice found 427 who were coached and 2733 who were uncoached.2º Looking at their Math scores on the first and second tries, we have these summary statistics: Coached Uncoached n 427 2733 x 521 505 Try 1 S 100 101 x 561 527 Try 2 S 100 101 x 40 Gain 22 S 58 250 The summary statistics for Gain are based on the changes in the scores of the individual students. Let's first ask if students who are coached increased their scores significantly. a. You could use the information on the Coached line 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? b. Carry out the proper test. What do you conclude? c. Give a 99% confidence interval for the mean gain of all students who are coached.