Before a championship football game, the referee is given a special commemorative coin to toss to decide which team will kick the ball first. Two minutes before game time, he receives an anonymous tip that the captain of one of the teams may have substituted a biased coin that has a 70% chance of show-ing heads each time it is tossed. The referee has time to toss the coin 10 times to test it. He decides that if it shows 8 or more heads in 10 tosses, he will reject this coin and replace it with another coin. Let p be the probability that this coin shows heads when it is tossed once.
a. Formulate the relevant null and alternative hypotheses (in terms of p) for the referee's test.
b. Using the referee's decision rule, find for this test.