Question

Use the Wilcoxon Signed Rank Sum Test for the following matched pairs of samples to determine

whether the two population locations differ at the 0:10 significance level.

Sample 1 9 12 13 8 7 10 9 12 13 8 7

Sample 2 5 10 11 9 3 9 5 10 11 9 3

Which one of the following statements is incorrect?

1. H0 : The two population locations are the same.

H1 : The location of population 1 is different from the location of population 2.

2. T

C D 62 and T

Answer 1

From the given data we need to determine whether the location of population 1 differs from the population 2 by performing a Wilcoxon sign rank sum test.

To test the claim the null and alternative hypothesis are defined as follows:

H₀: The two population locations are the same.

H₁: The location of population 1 is different from the location of population 2.

The necessary calculations are shown in the following table.

Therefore, the rank sums of the positive and negative differences are

$T^+=37.5 \\ T^- = 3 \\ n=11 \\ w_{stat} =min(T) = 3 \\ α=0.10$

Two-tailed test

From Wilcoxon Signed-Ranks Table

$w_{crit} = 13 \\ w_{stat}<w_{crit}$

Reject H₀.

We have sufficient evidence to conclude that the location of population 1 is different from the location of population 2.