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

question 59

Multiple Choice

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.

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