The following data relate the scores of 10 students on a college entrance examination to their grade-point average at the end of their first year.
Entrance examination score
Grade-point average
88
3.2
74
2.7
70
2.3
77
2.9
83
2.8
94
3.6
92
3.0
81
85
3.3
3.1
(a) Predict the grade-point average of a student, not listed in the given data, who scored 88 on the entrance examination.
(b) Obtain a 90 percent prediction interval for the score of the student described in part (a).
(c) Test the hypothesis, at the 5 percent level of significance, that a student’s grade-point average is independent of her or his score on the entrance examination.
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