Karscig claims that the average exam score on a 3801 class' first exam will be the same as the average score on the second exam. Forty exam 1 scores are randomly chosen and thirty-two exam 2 scores are selected. Both sets of scores are given below:
|
Exam 1
|
|
68
|
63
|
64
|
71
|
60
|
78
|
65
|
60
|
51
|
48
|
|
67
|
62
|
69
|
79
|
76
|
74
|
69
|
68
|
73
|
75
|
|
41
|
68
|
66
|
64
|
73
|
80
|
76
|
70
|
66
|
79
|
|
74
|
69
|
77
|
68
|
70
|
64
|
74
|
68
|
60
|
51
|
|
|
|
|
|
|
|
|
|
|
|
|
Exam 2
|
|
69
|
70
|
64
|
79
|
74
|
75
|
69
|
67
|
68
|
|
|
60
|
70
|
66
|
73
|
76
|
71
|
76
|
79
|
69
|
|
|
73
|
80
|
68
|
59
|
66
|
72
|
78
|
77
|
79
|
|
|
66
|
73
|
78
|
65
|
75
|
|
|
|
|
|
Test Karscig's claim (from our last exam) that the average exam score for Exam 1 was 70 using a two-tail test and a2% level of significance.
Test the hypothesis that there is no difference in the mean scores of Exam 1 and Exam 2 against the alternative that the average is greater for the second exam. Assume both sets of exam scores are normally distributed will 1 = 8.55 and 2 = 5.70 and use a 1% level of significance.
Then, test whether the proportion of exam I scores that arc at least 80% is the same as the proportion of exam 2 scores that are at least 80% using a two-tailed test and a 10% level of significance (Remember, these exams are 80 points total).