Using data set from 1.19

Yi Xi

3.897 21
3.885 14
3.778 28
2.54 22
3.028 21
3.865 31
2.962 32
3.961 27
0.5 29
3.178 26
3.31 24
3.538 30
3.083 24
3.013 24
3.245 33
2.963 27
3.522 25
3.013 31
2.947 25
2.118 20
2.563 24
3.357 21
3.731 28
3.925 27
3.556 28
3.101 26
2.42 28
2.579 22
3.871 26
3.06 21
3.927 25
2.375 16
2.929 28
3.375 26
2.857 22
3.072 24
3.381 21
3.29 30
3.549 27
3.646 26
2.978 26
2.654 30
2.54 24
2.25 26
2.069 29
2.617 24
2.183 31
2 15
2.952 19
3.806 18
2.871 27
3.352 16
3.305 27
2.952 26
3.547 24
3.691 30
3.16 21
2.194 20
3.323 30
3.936 29
2.922 25
2.716 23
3.37 25
3.606 23
2.642 30
2.452 21
2.655 24
3.714 32
1.806 18
3.516 23
3.039 20
2.966 23
2.482 18
2.7 18
3.92 29
2.834 20
3.222 23
3.084 26
4 28
3.511 34
3.323 20
3.072 20
2.079 26
3.875 32
3.208 25
2.92 27
3.345 27
3.956 29
3.808 19
2.506 21
3.886 24
2.183 27
3.429 25
3.024 18
3.75 29
3.833 24
3.113 27
2.875 21
2.747 19
2.311 18
1.841 25
1.583 18
2.879 20
3.591 32
2.914 24
3.716 35
2.8 25
3.621 28
3.792 28
2.867 25
3.419 22
3.6 30
2.394 20
2.286 20
1.486 31
3.885 20
3.8 29
3.914 28
1.86 16
2.948 28

(a) Obtain a 90% interval estimate for the mean freshman GPA for students whose ACT test score is 24. Interpret it in a sentence.
(b) Mabel obtained a 25 on the ACT test. Predict her freshman GPA using a 98% prediction interval. Interpret it in a sentence. Is your interval wider than the one in part (a)? Should it be?
(c) Determine the boundary values of the 90% confidence band for the regression line when xh = 25. Is your confidence band wider at this point than the interval in part (a)? Should it be?