The midterm and final examination scores for a sample of stu

The midterm and final examination scores for a sample of students in a Statistics class are given. Do the
data indicate that student performances differ on the two examinations? Use a 0.1 level of significance.
(Use Wilcoxon signed rank test).

Student Midterm Final
1 72 81
2 55 62
3 80 80
4 60 62
5 80 77
6 75 92
7 81 84
8 92 92
9 90 94
10 73 78
11 71 70
12 78 87

Solution

Prepare table as follows:

W value = 4.5

Mean difference = 16.3

Sum of positive ranks = 4.5

Sum of negative ranks = 50.5

z statistic = -2.344

Mean of W = 27.5

Std dev of W = 9.81

n = Sample size = 10

For z =-2.344 p value =0.01928.

As p <0.10, difference between the two is statistically significant.

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The critical value of W for N = 10 at p 0.1 is 8. Therefore, the result is significant at p 0.1