I have two non-calculating stats questions that I need help on, please!
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
n x1 s1 x2 s2 x s
Coached 427 500 92 529 97 29 59
Uncoached 2733 506 101 527 101 21 52
1. 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 mismatched pairs t test using Gain. Which is the correct one? Why?
2. The data you used came from a random sample of students who took the SAT twice. The response rate was 63%, which is pretty good for nongovernmental surveys, so let's accept that the respondents do represent all students who took the exam twice. Nonetheless, we can't be sure that coaching actually caused the coached students to gain more than the uncoached students. Explain briefly but clearly why this is so.
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
n x1 s1 x2 s2 x s
Coached 427 500 92 529 97 29 59
Uncoached 2733 506 101 527 101 21 52
1. 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 mismatched pairs t test using Gain. Which is the correct one? Why?
2. The data you used came from a random sample of students who took the SAT twice. The response rate was 63%, which is pretty good for nongovernmental surveys, so let's accept that the respondents do represent all students who took the exam twice. Nonetheless, we can't be sure that coaching actually caused the coached students to gain more than the uncoached students. Explain briefly but clearly why this is so.