For a random sample of 40, if 30 values are below the median and 10 are above, compute the test statistic.test.
A) -1.5
B) 1.66
C) -3.00
D) 3.32

Question

Quizplus · Accepted Answer

The test statistic for the Wilcoxon signed-rank test can be computed using the formula:
T = min(U, n*(n+1)/2 - U)
where U is the smaller of the two sums of ranks for the positive and negative differences, respectively.
In this case, there are 30 values below the median and 10 values above, so the median is the 20th value. The ranks for the 30 values below the median are 1, 2, 3, ..., 30. The ranks for the 10 values above the median are 21, 22, 23, ..., 30. The sum of ranks for the negative differences is:
1 + 2 + ... + 30 = 465
The sum of ranks for the positive differences is:
21 + 22 + ... + 30 = 255
Therefore, U = 255, and the test statistic is:
T = min(255, 40*(40+1)/2 - 255) = min(255, 820) = 255
To find the p-value for this test statistic, we can use a table of critical values or a calculator. Assuming a two-tailed test and a significance level of 0.05, we get a critical value of 23. Therefore, since our test statistic (255) is greater than the critical value (23), we reject the null hypothesis and conclude that there is a significant difference between the median and the sample values. The direction of the difference is not specified in this case.

For a Random Sample of 40, If 30 Values Are