Which of the Following Statements Are True?
A) the Wilcoxon $H _ { 0 } : \mu _ { 1 } - \mu _ { 2 } = \Delta _ { 0 }$

question 22

Multiple Choice

Which of the following statements are true?

• A) The Wilcoxon rank-sum test for testing \(H _ { 0 } : \mu _ { 1 } - \mu _ { 2 } = \Delta _ { 0 }\)
• Is carried out by first combining the \(\left( X _ { i } - Δ _ { 0 } \right) ^ { \prime } \text { sand } Y _ { i } ^ { \prime } \text { s }\)
• Into one sample of size m + n and ranking them from smallest (rank 1) to largest (rank m + n). The test statistic W is then the sum of the ranks of the \(\left( X _ { i } - \Delta _ { 0 } \right) ^ { \prime \mathrm { s } }\)
• B) The Wilcoxon rank-sum interval is very similar to the Wilcoxon signed=rank interval; the later uses pairwise averages from a single sample, whereas the former uses pairwise differences from two samples
• C) The Wilcoxon rank-sum interval is quite efficient with respect to the t interval.
• D) For large samples, the Wilcoxon rank-sum interval will tend to be only a bit longer than the t interval when the underlying populations are normal, and may be considerably shorter than the t interval if the underlying populations have heavier tails than do normal populations.
• E) All of the above statements are true.