Which of the following statements are true?
A) The Wilcoxon rank-sum test procedure is not distribution-free because it will not have the desired level of significance for a very large class of underlying distributions.
B) If there are three observed values of x and five observed values of y, then the smallest possible value of the Wilcoxon rank-sum test statistic W is w = 6 and the largest possible value is w = 21.
C) When the distributions being sampled are both normal with $\sigma _ { 1 } - \sigma _ { 2 } ,$
And therefore have the same shapes and spreads, only the pooled t test can be used in testing $H_{1}: \mu_{4}-\mu_{1}=\square_{0}$

Whereas the Wilcoxon rank-sum test should not be used because it is distribution-free.
D) When normality and equal variances both hold, the Wilcoxon rank-sum test is approximately 75% as efficient as the pooled t test in large samples.
E) All of the above statements are true.

Question

Which of the following statements are true?
A) The Wilcoxon rank-sum test procedure is not distribution-free because it will not have the desired level of significance for a very large class of underlying distributions.
B) If there are three observed values of x and five observed values of y, then the smallest possible value of the Wilcoxon rank-sum test statistic W is w = 6 and the largest possible value is w = 21.
C) When the distributions being sampled are both normal with $\sigma _ { 1 } - \sigma _ { 2 } ,$
And therefore have the same shapes and spreads, only the pooled t test can be used in testing $H_{1}: \mu_{4}-\mu_{1}=\square_{0}$

Whereas the Wilcoxon rank-sum test should not be used because it is distribution-free.
D) When normality and equal variances both hold, the Wilcoxon rank-sum test is approximately 75% as efficient as the pooled t test in large samples.
E) All of the above statements are true.

Quizplus · Accepted Answer

The Wilcoxon rank-sum test is a non-parametric test and is distribution-free, making statement A false. Statement B is true as it correctly describes the range of the Wilcoxon rank-sum test statistic W for the given sample sizes. Statement C is incorrect because the Wilcoxon rank-sum test can be used regardless of distribution assumptions. Statement D is incorrect as the efficiency of the Wilcoxon rank-sum test compared to the t-test is typically around 95% under normality, not 75%. Statement E is false because not all statements are true.

Which of the Following Statements Are True? A) the Wilcoxon σ1−σ2,\sigma _ { 1 } - \sigma _ { 2 } ,σ1​−σ2​,

Which of the Following Statements Are True?
A) the Wilcoxon $\sigma _ { 1 } - \sigma _ { 2 } ,$