Test on a single median] Determine if, at the 5% level of significance, it is re
ID: 3309722 • Letter: T
Question
Test on a single median] Determine if, at the 5% level of significance, it is reasonable to say that the median of a given set of data is 23 if: 5· a. Out of 115 data points, 46 are less than 23, 10 are at 23, and the other 59 are larger. b. Out of 76 data points, 29 are less than 23, 20 are at 23, and the other 27 are larger. c. Out of 218 data points, 79 are less than 23, 9 are at 23, and the other 130 are larger Show the results and conclusions of each test (total.et.& evaluations), plus your final conclusions for each case.Explanation / Answer
a)
We used Minitab for our calculation.
Out of 115 observations. 46 are less than 23, 10 are = 23 and 59 are greater than 23.
The non-parametric test used to check the null hypothesis that the median is 23 is Wilcoxon 1 Sample signed rank test.
The output of the test is as under.
Wilcoxon Signed Rank Test: Sample 1
Test of median = 23.00 versus median not = 23.00
N for Wilcoxon Estimated
N Test Statistic P Median
Sample 1 115 104 1711.0 0.001 22.50
P-Value is less than 0.05 hence we conclude that median is not 23 it's 22.50
b)
The output for second sample 2 is
Wilcoxon Signed Rank Test: Sample 2
Test of median = 23.00 versus median not = 23.00
N for Wilcoxon Estimated
N Test Statistic P Median
Sample 2 76 46 153.0 0.000 22.50
P-Value is less than 0.05 hence we conclude that median is not 23 it's 22.50
c)
The output for second sample 3 is
Wilcoxon Signed Rank Test: Sample 3
Test of median = 23.00 versus median not = 23.00
N for Wilcoxon Estimated
N Test Statistic P Median
Sample 3 218 209 8515.0 0.005 22.50
P-Value is less than 0.05 hence we conclude that median is not 23 it's 22.50
All the three samples don't have median equal to 23.
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