Consider Example 13 about the power of the test of H₀: p = 0.1 against H_a: p > 0.1 used to test the effectiveness of a manual therapy in opening blocked tubes, where p is the probability of at least one unblocked tube after therapy. Another statement in that grant proposal read as follows: “However, if the patency rate is only 20%, the power of the test drops to 60%.”
a. How should the power of 60% be interpreted?
b. In context, what is a Type II error for this trial?
c. What is the probability of committing a Type II error if p = 0.2?