Section 6.5 1. Coaching and SAT scores (from Moore, Basic Practice of Statistics) 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. The table below represents summary data for students who were coached: Try 1 Try 2 Gain X 1 $1 X 2 SZ S Coached n = 427 500 92 529 97 29 59 Two-sample SE = 6.45 One-sample SE = a. If we are looking for evidence that the Coached students improved on their second try, should we use a two-sample test comparing Try 1 and Try2 or a paired one-sample test using Gain? Explain your reasoning. b. Carry out the proper test. Show all steps