Which of the Following Statements Are True?
A) When the Data

question 14

Multiple Choice

Which of the following statements are true?

• A) When the data consists of pairs \(\left( X _ { 1 } , Y _ { 1 } \right) , \ldots \ldots , \left( X _ { n } , Y _ { n } \right)\)
• And the differences \(D _ { i } = X _ { i } - Y _ { i }\)
• (i = 1, . . . . . . ,n )
• Are not assumed to be normally distributed, hypotheses tests about the expected differences \(\mu _ { D }\)
• Can be tested by using the Wilcoxon signed-rank test on the \(D _ { i } ^ { \prime } \text { s }\)
• Provided that the distribution of the differences is continuous and symmetric.
• B) When the sample size n is larger than 20, it can be shown that the Wilcoxon signed-rank test statistic \(S _ { + }\)
• Has approximately a normal distribution when the null hypothesis is true.
• C) When the underlying distribution being sampled is normal, either the t test or the Wilcoxon signed-rank test can be used to test a hypothesis about the population mean \(\mu .\)
• D) A number of different efficiency measures have been proposed by statisticians; one that many statisticians regard as credible is called asymptotic relative efficiency (ARE).
• E) All of the above statements are true.

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