Using a p level of 0.05, a researcher performed the Wilcoxon signed-rank test with a sample size of 16 and found that the sum of the ranks for positive differences was 36 and the sum of the ranks for negative differences was 100.Which statement accurately describes the results of the hypothesis test for these data?
A) Reject the null because the test statistics sum to above 100.
B) The test statistic is larger than the critical cutoff, which is 29, so fail to reject the null hypothesis.
C) The test statistic is larger than the critical cutoff, which is 29, so reject the null hypothesis.
D) Fail to reject the null hypothesis because 36 is less than 100.

Question

Quizplus · Accepted Answer

The Wilcoxon signed-rank test is a nonparametric test used to compare two related samples. In this case, the null hypothesis is that the median of the differences between the paired observations is zero. The test statistic is the sum of the ranks for the positive differences or the sum of the ranks for the negative differences, whichever is smaller.

In this case, the sum of the ranks for positive differences is 36 and the sum of the ranks for negative differences is 100. The test statistic is the smaller of these two values, which is 36.

To determine whether to reject or fail to reject the null hypothesis, we compare the test statistic to the critical cutoff value from a table. For a sample size of 16 and a p level of 0.05, the critical cutoff is 29. Since the test statistic of 36 is larger than the critical cutoff value of 29, we fail to reject the null hypothesis. Therefore, the correct answer is B.

Using a P Level of 0