A study compares a new drug for pain relief in patients with chronic migraine against a placebo. Each patient is given both the drug and the placebo (in random order) and reports which one works better. Let p denote the probability that the pain relief is better with the drug. You have to decide whether you can reject H₀: p = 0.50 in favor of H_a: p ≠ 0.50 based on seeing the results of one patient after another. Ahead of time, you have no idea whether the drug or placebo works better, and you assume they are equally effective (i.e., you assume the null hypothesis is true.) Each student should indicate
a. How many consecutive patients reporting better relief with the drug would be necessary before he or she would feel comfortable rejecting H₀: p = 0.50 in favor of H_a: p ≠ 0.50 and concluding that the drug works better.
b. How many consecutive patients reporting better relief with the placebo would be necessary before he or she would feel comfortable rejecting H₀: p = 0.50 in favor of H_a: p ≠ 0.50 and concluding that the placebo works better. The instructor will compile a “distribution of significance levels” for the two cases. Are they the same? In principle, should they be?