Question: (24 points) A statistics professor has devised a diagnostic quiz, which, when given during the first class, can accurately predict a student's performance on the final exam. So far data are available for 10 students as follow:

Student Quiz Score Final Exam Score

1 5 82

2 8 80

3 3 75

4 1 60

5 10 92

6 6 85

7 7 86

8 4 70

9 2 42

10 6 78

(a) Find the correlation coefficient r.

(b) Find the test statistic t for testing the statistical significance of r.

(c) Find the critical t value for a two-tailed test, with \(\alpha \) = 0.05. Is the r value you found statistically significant?

(d) Find the regression equation for predicting the final exam score from the quiz.

(e) What final exam score would be predicted for a student who scored a 9 on the quiz?