Recall, that the significance level of a test is the probability that the null hypothesis is rejected if it is, in fact, true. The power of a hypothesis test is defined as the probability that the null hypothesis will be rejected if it is, in fact, false. Suppose an exact Binomial test is to be conducted to test

H0 : p = 1 /2 vs. Ha : p < 1/ 2

Twenty trials are conducted and the null hypothesis is rejected in favor of the alternative if six or fewer successes are observed. Here p denotes the probability of a success in each trial.

(a) Find the significance level of this testing procedure.

(b) Suppose that in fact p = 1 /3 . In this case what is the power of the test?