Question

17-14: The following sample data have been collected from independent samples from independent samples from two populations. The claim is that the first population median will be larger than the median of the second population.

            Sample 1                    Sample 2

            4.4       2.6                   3.7       4.2

            2.7       2.4                   3.5       5.2

            1.0       2.0                   4.0       4.4

            3.5       2.8                   4.9       4.3

            2.8                               3.1

1. State the appropriate null and alternative hypotheses.
2. Using the Mann-Whitney U-test, based on the sample data, what should you conclude about the null hypothesis? Test using α=0.05.

Answer 1

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Rank	sample		Rank	Sample
1	sample_1		3.1	sample_2
2	sample_1		3.5	sample_2
2.4	sample_1		3.7	sample_2
2.6	sample_1		4	sample_2
2.7	sample_1		4.2	sample_2
2.8	sample_1		4.3	sample_2
2.8	sample_1		4.4	sample_2
3.5	sample_1		4.9	sample_2
4.4	sample_1		5.2	sample_2
24.2	Sum		37.3	Sum

Rank	Score	Sample
1	1	sample_1
2	2	sample_1
3	2.4	sample_1
4	2.6	sample_1
5	2.7	sample_1
6	2.8	sample_1
7	2.8	sample_1
8	3.1	sample_2
9	3.5	sample_1
10	3.5	sample_2
11	3.7	sample_2
12	4	sample_2
13	4.2	sample_2
14	4.3	sample_2
15	4.4	sample_1
16	4.4	sample_2
17	4.9	sample_2
18	5.2	sample_2