Question

In: Statistics and Probability

The Dean of the Business School at State University would like to test the hypothesis that...

The Dean of the Business School at State University would like to test the hypothesis that no difference exists between the average final exam grades for the Introduction to Marketing course and the Introduction to Finance course. A random sample of eight students who took both courses was selected and their final exam grades for each course are shown below. Assume Population 1 is defined as the Marketing exam scores and Population 2 is defined as the Finance exam scores. Which one of the following statements is​ true?

Student

1

2

3

4

5

6

7

8

Marketing

82

86

74

93

90

76

87

100

Finance

76

91

70

79

96

70

85

81

A.

Because the​ 95% confidence interval includes​ zero, we can conclude that no difference exists between the average final exam grades for the Introduction to Marketing course and the Introduction to Finance course.

B.

Because the​ 95% confidence interval does include​ zero, we cannot conclude that a difference exists between the average final exam grades for the Introduction to Marketing course and the Introduction to Finance course.

C.

Because the​ 95% confidence interval includes​ zero, we cannot conclude that no difference exists between the average final exam grades for the Introduction to Marketing course and the Introduction to Finance course.

D.

Because the​ 95% confidence interval does not include​ zero, we can conclude that a difference exists between the average final exam grades for the Introduction to Marketing course and the Introduction to Finance course.

Solutions

Expert Solution

Marketing ( X ) Finance ( Y )
82 16 76 25
86 0 91 100
74 144 70 121
93 49 79 4
90 16 96 225
76 100 70 121
87 1 85 16
100 196 81 0
Total 688 522 648 612

Mean

Standard deviation

Sample variance = 74.5714

Mean

Standard deviation

Sample variance = 87.4286

To Test :-

H0 :-  

H1 :-  

Confidence interval :-



DF = 13



Lower Limit =
Lower Limit = -4.7217
Upper Limit =
Upper Limit = 14.7217
95% Confidence interval is ( -4.7217 , 14.7217 )

Option  A  is correct.

Because the​ 95% confidence interval includes​ zero, we can conclude that no difference exists between the average final exam grades for the Introduction to Marketing course and the Introduction to Finance course.

orchestra answered 1 year ago
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