Question

Eight observations were randomly selected from populations that were not necessarily normally distributed. Use the 0.05 significance level, a two-tailed test, and the Wilcoxon rank-sum test.

Population A:	38	45	56	57	61	69	70	79
Population B:	26	31	35	42	51	52	57	62

State the decision rule. Use the 0.05 significance level.

H₀: The distributions are the same.
H₁: The distributions are not the same.

Complete the following table.

Score Rank Score Rank 0.0 0.0

What is the Wilcoxon rank-sum test value?

What is your decision regarding H₀? Is there a difference between the two populations?

Answer 1

Following table shows the combined data with ranks:

Population	Score	Rank
B	26	1
B	31	2
B	35	3
A	38	4
B	42	5
A	45	6
B	51	7
B	52	8
A	56	9
A	57	10.5
B	57	10.5
A	61	12
B	62	13
A	69	14
A	70	15
A	79	16

Following table shows the rank sum  :

Score (A)	Rank	Score (B)	Rank
38	4	26	1
45	6	31	2
56	9	35	3
57	10.5	42	5
61	12	51	7
69	14	52	8
70	15	57	10.5
79	16	62	13
Total	86.5		49.5

Now we have

$U_{2}=n_{1}n_{2}+rac{n_{2}(n_{2}+1)}{2}-R_{2}=64+36-49.5=50.5$

The test statistics is

U = 13.5

The critical value for test statistics for alpha = 0.05 is 13.

Since U > 13 so we reject the null hypothesis. There is no difference between the two populations.