Suppose that the null hypothesis is true, that the distribution of the test statistic, T say, is continuous with cdf F and that the test rejects for large values of T . Let V denote the p-value of the test.
a. Show that V = 1 − F(T ).
b. Conclude that the null distribution of V is uniform. (Hint: See Proposition C of Section 2.3.)
c. If the null hypothesis is true, what is the probability that the p-value is greater than .1?
d. Show that the test that rejects if V < α has significance level α.
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