# Wilcoxon Sign Rank Test rejection region

1. Dec 30, 2017

### tzx9633

1. The problem statement, all variables and given/known data
Two computer software packages are being considered for use in the inventory control department of a small manufacturing firm. The firm has selected 12 different computing task that are typical of the kinds of jobs. The results are shown in the table below. At the 0.05 level, can we conclude that those two computer software packages are identical?

1.Ho: those two computer software packages are identical
H1: those two computer software packages are not same

2. Based on the alternative hypothesis, the test is min (〖 T〗^+, 〖 T〗^-) = min(8.5, 57.5) = 8.5

3.α = 0.05, n = 12 – 1 = 11

. From table of Wilcoxon signed rank for two tail test,

α = 0.05, n = 11, then a = 14

We will reject Ho if min (〖 T〗^+, 〖 T〗^-) ≤ a

5. Since min(8.5, 57.5) = 8.5 ≤ 14, thus we reject Ho and conclude that the software packages are not equally rapid in handling computing tasks like those in the sample, or the population median for 〖di=x〗_i-y_i is not equal to zero and that package x is faster than package y in handling computing task like ones sample.

2. Relevant equations

3. The attempt at a solution

In this question , we already knew that it's 2 tailed test , why the author still use α = 0.05 , not α/2 = 0.025 ??? I think it's wrong ...

I think we should use α/2 = 0.025 when finding the U critical

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2. Dec 30, 2017

### FactChecker

If you are using a table for the Wilcoxon signed rank for two tail test you should not have to make any adjustments of the α value. The table should already have adjusted for that.