Question

Ouestion Help A null hypothesis, alternative hypothesis, and sample from the population under consideration are provided below. Use the Wilcoxon signed-rank tost to perform the required hypothesis test at the 5% significance level Ho: 1-6, H,: 46 15 10 9 14 12 20 ! Click here to view a table of values of W The test statistic is W-D (Round to one decimal place as needed) Identify the critical value(s). Select the correct choice below and fill in the answer box within your choice O A. The critical values are and (Use ascending order) OB. The critical value is the null hypothesis. The data sufficient evidence to conclude that the meanis

Answer 1

Ans : To perform The Wilcoxon signed test for given data

15

3

10

9

14

17

20

7

To test :

H₀ : $\mu$ = 6 versus H_a : $\mu$ > 6

mean	15	3	10	9	14	17	20	7
Difference	9	-3	4	3	8	11	14	1

Ignoring the signs, rank the differences smallest rank =1

mean	15	3	10	9	14	17	20	7
Difference	9	-3	4	3	8	11	14	1
Rank	6	2.5	4	2.5	5	7	8	1

positive rank and negative ranks are

mean	15	3	10	9	14	17	20	7
Difference	9	-3	4	3	8	11	14	1
-+Rank	6		4	2.5	5	7	8	1
- Rank		2.5

Therefore ,

sum of + rank = 33.5

sum of -rank =2.5

minimum os them is 2.5

Test Statistics :

W = 2.5

Critical values :

significance level =0.05

then critical value = 4

Since test statistic value < critical value then reject the null hypothesis at 0.05 significance level

Ans :

Reject the null hypothesis the data is sufficient evidence to conclude that the mean is greater than 6