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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Definitions:

Chlorine Atom

A chemical element with symbol Cl and atomic number 17, known for its roles in various chemical reactions and compounds.

Neutrons

Neutral particles found in the nucleus of an atom, contributing to the atom's mass but not its charge.

Protons

Positively charged subatomic particles found in the nucleus of an atom.

Amu

Atomic Mass Unit, a unit of mass used to express atomic and molecular weights, equivalent to one twelfth of the mass of a carbon-12 atom.