In their book Freakonomics, Levitt and Dubner (2005) describe a study conducted by Duggan and Levitt (2002) that broached the question: Do sumo wrestlers cheat? Sumo wrestlers garner enormous respect in Japan, where sumo wrestling is considered the national sport. The researchers examined the results of 32,000 wrestling matches over an 11-year time span. If a wrestler finishes a tournament with a losing record (7 or fewer wins out of 15 matches), his ranking goes down, as do the money and prestige that come with winning. The researchers wondered whether, going into the last match of the tournament, wrestlers with 7-7 records (needing only 1 more win to rise in the rankings) would have a better-than-expected win record against wrestlers with 8-6 records (those who already are guaranteed to rise in the rankings). Such a phenomenon might indicate cheating. One 7-7 wrestler (wrestler A), based on past matches against a given 8-6 opponent (wrestler B), was calculated to have won 48.7% of the time. 

a. If there is no cheating, what is the probability that wrestler A will beat wrestler B in any situation, including the one in which A is 7-7 and B is 8-6? 

b. If matches tend to be rigged so that 8-6 wrestlers frequently throw matches to help other wrestlers maintain their rankings (and to get payback from 7-7 wrestlers in future matches), what would you expect to happen to the winning percentage when these two wrestlers meet under these exact conditions—that is, the first is 7-7 in the tournament and the second is 8-6?

c. State the null hypothesis and research hypothesis for the study examining whether sumo wrestlers cheat. 

d. In this particular real-life example, wrestler A was found to have beaten wrestler B 79.6% of the time when A had a 7-7 record and B had an 8-6 record. If inferential statistics determined that it was very unlikely that this would happen by chance, what would your decision be? Use the language of hypothesis testing.