Answer to Question #226080 in Statistics and Probability for Carrie

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.