Suppose a researcher routinely conducts tests using a nominal probability of Type I error of .05, rejecting Ho if the P-value satisfies P < .05. Suppose an exact test using X2 has null distribution P(X2 = 0) = .30, P(X = 3) = .62, and P(X29) .08.

a. Show that, with the usual P-value, the actual probability of Type I error equals O.

b. Show that, with the mid P-value, the actual probability of Type I error equals .08.

c. Repeat

(a) and

(b) using the probabilities .30, .66, .04. Note that the test with mid P-value can be "conservative" or "liberal." The test with the ordinary P-value cannot be liberal.