NCAA March Madness. For three weeks each March the National Collegiate Athletic Associatio...

NCAA March Madness. For three weeks each March the National Collegiate Athletic Association (NCAA) holds its annual men’s basketball championship tournament The 64 best college basketball teams in the nation play a single-elimination tournament—a total of 63 games—to determine the NCAA champion. Tournament followers from hard-core gamblers to the casual fan who enters the office betting pool, have a strong interest in handicapping the games. To provide insight into this phenomenon, statisticians Hal Stern and Barbara Mock analyzed data from 13 previous NCAA tournaments and published their results in Chance (Winter 1998). The results of first-round games are summarized in the table on p. 347.

a. A common perception among fans, the media, and gamblers is that the higher seeded team has a better than 50-50 chance of winning a first-round game. Is there evidence to support this perception? Conduct the appropriate test for each matchup. What trends do you observe?

---

b. Is there evidence to support the claim that a 1-, 2-, 3-, or 4-seeded team will win by an average of more than 10 points in first-round games? Conduct the appropriate test for each matchup.

---

c. Is there evidence to support the claim that a 5-, 6-, 7-, or 8-seeded team will win by an average of less than 5 points in first-round games? Conduct the appropriate test for each matchup.

---

d. The researchers also calculated the difference between the outcome of the game (victory margin, in points) and the point spread established by Las Vegas oddsmakers for a sample of 360 recent NCAA tournament games. The mean difference is .7 and the standard deviation of the difference is 11.3. If the true mean difference is 0, then the point spread can be considered a good predictor of the outcome of the game. Use this sample information to test the hypothesis that the point spread, on average, is a good predictor of the victory margin in NCAA tournament games.