70. A test of whether or not 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 signi cance 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. Determine the power of the test with rejection region R2. Is this test 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?