The following are the ratings (0 to 4) given by 12 individuals for two possible new flavors of soft drinks.
Wilcoxon rank-sum is to be used. At the 0.05 level of significance, what is the decision?
A) Fail to reject null hypothesis; critical value is $\pm$1.65
B) Fail to reject null hypothesis; critical value is $\pm$1.96
C) Reject null hypothesis; critical value is 0.1732
D) Reject null hypothesis; critical value is 0.3464

Question

The following are the ratings (0 to 4) given by 12 individuals for two possible new flavors of soft drinks. 
 Wilcoxon rank-sum is to be used. At the 0.05 level of significance, what is the decision?
A) Fail to reject null hypothesis; critical value is $\pm$1.65 
B) Fail to reject null hypothesis; critical value is $\pm$1.96 
C) Reject null hypothesis; critical value is 0.1732 
D) Reject null hypothesis; critical value is 0.3464

Quizplus · Accepted Answer

The Wilcoxon rank-sum test is used to compare two independent samples. The null hypothesis is that there is no difference between the two groups. The alternative hypothesis is that there is a difference. The critical value for a two-tailed test at the 0.05 level of significance with 12 observations in each group is 101.96. If the test statistic is less than or equal to the critical value, we fail to reject the null hypothesis. If the test statistic is greater than the critical value, we reject the null hypothesis. In this case, the critical value given in choice B is correct and we fail to reject the null hypothesis. None of the other choices provide the correct critical value or decision.

The Following Are the Ratings (0 to 4) Given by 12