Answer to Question #226082 in Statistics and Probability for Carrie

Question

Use the Wilcoxon sign test on the data below to determine at the 5% significance level whether the

locations of the two populations differ. Assume that the two samples selected come two popula-

tions that are normally distributed.

Sample 1 32 22 18 29 20 34 25 9 28 17

Sample 2 29 20 18 27 29 23 19 12 22 10

Which one of the following statements is incorrect?

1. The two population locations are the same.

2. The location of population 1 is to the left of the population location 2.

3. The number of positive differences is 7.

4. The test statistic Z is 1.6667

5. The p-value for one-tailed test is 0.095.

Answer 1

• Step1. Set up hypotheses and determine level of significance.

H₀: The median difference is zero versus

H₁: The median difference is not zero α=0.05

• Step 2. Select the appropriate test statistic.

The test statistic for the Wilcoxon Signed Rank Test is W, defined as the smaller of W+ and W- which are the sums of the positive and negative ranks, respectively. 

• Step 3. Set up the decision rule.

The critical value of W can be found in the table of critical values. To determine the appropriate critical value from Table 7 we need sample size (n=15) and our two-sided level of significance (α=0.05). The critical value for this two-sided test with n=15 and α=0.05 is 25 and the decision rule is as follows: Reject H₀ if W < 25.

• Step 4. Compute the test statistic.

 Because the before and after systolic blood pressures measures are paired, we compute difference scores for each patient.