Question

30 21 == ននន 22 Suppose you want to compare two treatments, A and B. Use the Wilcoxon rank sum test to determine whether the distribution for population is shifted to the left of the distribution for population Sample Sample a. Specify the null and alternative hypotheses you would test. b. Suppose you obtained the independent random samples of observations on experimental units subjected to the two treatments shown in the table to the night. Conduct atest of the hypotheses described in part a. Test using a 0.025 31 Click the icon to view the critical values of T, and Tu for the Wilcoxon rank sum test for independent samples. 20 34 32 40 35 a. What are the null and alternative hypotheses? Ho: The probability distribution for population is the probability distribution for population A He: The probability distribution for population Dis the probability distribution for population A b. Determine the test statistie. Select the correct choice below and fill in the answer box within your choice (Type an integer or a decimal.) ОАТ OB. TA- dentify the rejection region. Select the correct choice below and fill in any answer boxes within your choice. DATAS ов. Тgs

Answer 1

a. Ho : The probability distribution of B is equal to the probability distribution of A

H1: The probability distribution of B is equal to the probability distribution of A

b.

First, we put both samples together and organize it in ascending order, which is shown in the table below:

Sample	Value
2	21
2	22
1	28
2	30
1	31
1	32
1	33
1	34
1	35
1	36
2	36
1	40
1	41

Now, that the values that are in ascending order are assigned ranks to them, taking care of assigning the average rank to values with rank ties

Sample	Value	Rank	Rank (Adjusted for ties)
2	21	1	1
2	22	2	2
1	28	3	3
2	30	4	4
1	31	5	5
1	32	6	6
1	33	7	7
1	34	8	8
1	35	9	9
1	36	10	10.5
2	36	11	10.5
1	40	12	12
1	41	13	13

The sum of ranks for sample 1 is:

B. TA : R1​=3+5+6+7+8+9+10.5+12+13=73.5

and the sum of ranks of sample 2 is:

A. TB : R2​=1+2+4+10.5=17.5

Hence, the test statistic is R = R1​=73.5.

A. TA > = 73.5 and TB < = 73.5

tL = 15 and tU = 41

Since, test statistic > 41. Reject Ho, There is sufficient evidence that probability distribution of B lies to the left of distribution of A.

However, sample size is too small.

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