Question
Independent random samples of size n1 20 and n2 25 are drawn from non normal populations
1 and 2. The combined sample is ranked and T1 252. Use the large-sample approximation to
the Wilcoxon rank sum test to determine whether there is a difference in the two population
distributions. Calculate the p-value for the test. how specifically how is the p value calculated
and how do I use the z-score table to find that value?
Solution
Variables
n1=20n1=20: Sample size for group 1.
n2=25n2=25: Sample size for group 2.
T1=252T1=252: Sum of ranks for group 1.
Test Statistic
The test statistic T1 is compared to the expected rank sum under the null hypothesis.
Under the null hypothesis:
The two samples come from the same distribution.
The mean (μT) and standard deviation (σT) of T1 are:
n 1(n 1+ n 2+1)
μT =
2
σT ==
√ n1 n 2(n 1+n 2+1)
12
Substitute n1=20 and n2=25
Independent random samples of size n1 20 and n2 25 are drawn from non normal populations
1 and 2. The combined sample is ranked and T1 252. Use the large-sample approximation to
the Wilcoxon rank sum test to determine whether there is a difference in the two population
distributions. Calculate the p-value for the test. how specifically how is the p value calculated
and how do I use the z-score table to find that value?
Solution
Variables
n1=20n1=20: Sample size for group 1.
n2=25n2=25: Sample size for group 2.
T1=252T1=252: Sum of ranks for group 1.
Test Statistic
The test statistic T1 is compared to the expected rank sum under the null hypothesis.
Under the null hypothesis:
The two samples come from the same distribution.
The mean (μT) and standard deviation (σT) of T1 are:
n 1(n 1+ n 2+1)
μT =
2
σT ==
√ n1 n 2(n 1+n 2+1)
12
Substitute n1=20 and n2=25
