In 2007, NBA referee Tim Donaghy was suspected of collaborating with a bookie to fix games in which he was refereeing. To help fix a game, a referee could call more fouls on one team which would allow the other team to score more points. If gamblers knew of this fix before the game, they would bet on the team that would have fewer called fouls to win (the one the referee was favoring). There were 40 games in which the referee and the bookie were suspected of collaborating. In these 40 games Donaghy’s foul calls favored the team that received the heavier betting 28 times. We will assume there should be no relationship between fouls called on a team and heavy betting on the opposing team. Therefore, just by chance, we would expect about half the time Donaghy’s foul calls would favor the team that received the heaviest betting. We want to determine whether, assuming the chance model is true, it is very unlikely that Donaghy’s foul calls would favor the team that received heavier betting 28 out of 40 times. 

a. Describe how you could use coins to simulate the chance model. Give the number of coins you would use and what each side of the coin represents. 

b. Use the One Proportion applet to answer the question, “If the chance model is true, how likely is it that Donaghy’s foul calls would favor the team that received heavier betting 28 out of 40 times?” Explain how you determined your answer based on the results in the applet.