Question

Asked Jun 19, 2019

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The results of a pre-test and a post-test for ten students is given below. Is there a significant difference in the median score difference post-test-pre-test? Test with the Wilcoxon Signed-Rank Test with a 5% significance level. You may assume the distribution of differences is symmetric.

Pre-Test 75 62 83 71 75 78 82 83 80 65

Post-Test 91 60 83 72 80 92 79 85 80 79

Step 1

Denote *µ _{d}* as the median difference for post and pre-test.

*Hypotheses:*

*Null hypothesis*: The median difference is zero.

*Alternative hypothesis: *The median difference differs from zero.

It is given that the distribution of difference is symmetric. Therefore, Wilcoxon-signed rank test can be used here.

The necessary calculations for finding test statistic is given below:

Step 2

*The rank table is given below:*

Step 3

The sum of positive ranks is denoted as W+.

The sum of negative ranks is denoted as W-.

From the above table W+=1.5 + 1.5 + 3 + 4.5 + 7 + 8.5 + 8.5 + 10 = 44.5

W- = 4.5 + 6 = 10.5

*Test stat...*

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