A coin is to be spun 25 times. Let x the number of spins that result in heads (H). Consider the following rule for deciding whether or not the coin is fair:

Judge the coin to be fair if 8  x  17 Judge the coin to be biased if either x  7 or x  18

a. What is the probability of judging the coin to be biased when it is actually fair?

b. What is the probability of judging the coin to be fair when P(H) .9, so that there is a substantial bias?

Repeat for P(H) .1.

c. What is the probability of judging the coin to be fair when P(H) .6? when P(H) .4? Why are the probabilities so large compared to the probabilities in Part (b)?

d. What happens to the “error probabilities” of Parts

(a) and

(b) if the decision rule is changed so that the coin is judged fair if 7  x  18 and judged unfair otherwise? Is this a better rule than the one first proposed?