Question

At a large university, freshmen students are required to take an introduction to writing class. Students are given a survey on their attitudes towards writing at the beginning and end of class. Each student receives a score between 0 and 100 (the higher the score, the more favorable the attitude toward writing). The scores of nine different students from the beginning and end of class are shown below. Use the Wilcoxon signed-rank test to check at a 5% significance level whether the attitudes toward writing appear to increase by the end of the class?

Beginning	77.6	83.2	60.2	93.1	74.6	43.1	86.9	79.3	80.2
End	85.4	79.6	64.2	96.6	79.3	40.5	90.1	89.2	85.6

Answer 1

Beginning	End	difference=sample1-sample 2	absolue difference	rank	rank if positive	rank if negative
77.6	85.4	-7.8	7.8	8		8
83.2	79.6	3.6	3.6	4	4
60.2	64.2	-4	4	5		5
93.1	96.6	-3.5	3.5	3		3
74.6	79.3	-4.7	4.7	6		6
43.1	40.5	2.6	2.6	1	1
86.9	90.1	-3.2	3.2	2		2
79.3	89.2	-9.9	9.9	9		9
80.2	85.6	-5.4	5.4	7		7

Ho :median difference=   0
Ha: median difference >   0
  
Level of Significance , α =    0.05
  
number of non zero difference , n =    9
  
sum of positive ranks, W+ =    5
sum of negative ranks , W- =   40
  
T = W+ = 5

The critical value for the signficance level α=0.05 provided, and the type of tail specified is T∗ =8, and the null hypothesis is rejected if T≤8.

(3) Decision about the null hypothesis

Since in this case, T=5≤8, there is enough evidence to claim that the attitudes toward writing appear to increase by the end of the class, at the α=0.05 significance level.