Consider the Wilcox on signed-rank test, and suppose that n = 5. Assume that H0: = 0

Question:

Consider the Wilcox on signed-rank test, and suppose that n = 5. Assume that H0: μ = μ0 is true.
(a) How many different sequences of signed ranks are possible? Enumerate these sequences.
(b) How many different values of W+ are there? Find the probability associated with each value of W+.
(c) Suppose that we define the critical region of the test to be to reject H0 if w+ > w* and w* = 13. What is the approximate a level of this test?
(d) Does this exercise show how the critical values for the Wilcox on signed-rank test were developed? Explain.