A test of whether a coin is fair will be based on n = 50 tosses. Let X be the resulting number of heads. Consider two rejection regions: R₁ = {x: either x ≤ 17 or x ≥ 33} and R₂ = {x: either x ≤ 18 or x ≥ 37}.

a. Determine the significance level (type I error probability) for each rejection region.
b. Determine the power of each test when p = .49. Is the test with rejection region R₁ a uniformly most powerful level .033 test? Explain.
c. Is the test with rejection region R₂ unbiased? Explain.
d. Sketch the power function for the test with rejection region R₁, and then do so for the test with the rejection region R₂. What does your intuition suggest about the desirability of using the rejection region R₂?