Betting the Spreads. College basketball, and particularly the NCAA basketball tournament, is a popular venue for gambling, from novices in office betting pools to high rollers. To encourage uniform betting across teams, Las Vegas oddsmakers assign a point spread to each game. The point spread is the oddsmakers’ prediction for the number of points by which the favored team will win. If you bet on the favorite, you win the bet provided the favorite wins by more than the point spread; otherwise, you lose the bet. Is the point spread a good measure of the relative ability of the two teams? H. Stern and B. Mock addressed this question in the paper “College Basketball Upsets: Will a 16-Seed Ever Beat a 1-Seed?” (Chance, Vol. 11(1), pp. 27–31). They obtained the difference between the actual margin of victory and the point spread, called the point-spread error, for 2109 college basketball games. The mean point-spread error was found to be −0.2 point with a standard deviation of 10.9 points. For a particular game, a point-spread error of 0 indicates that the point spread was a perfect estimate of the two teams’ relative abilities. a. If, on average, the oddsmakers are estimating correctly, what is the (population) mean point-spread error? b. Use the data to decide, at the 5% significance level, whether the (population) mean point-spread error differs from 0. c. Interpret your answer in part (b).
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
Betting the Spreads. College basketball, and particularly the NCAA basketball tournament, is a popular venue for gambling, from novices in office betting pools to high rollers. To encourage uniform betting across teams, Las Vegas oddsmakers assign a point spread to each game. The point spread is the oddsmakers’ prediction for the number of points by which the favored team will win. If you bet on the favorite, you win the bet provided the favorite wins by more than the point spread; otherwise, you lose the bet. Is the point spread a good measure of the relative ability of the two teams? H. Stern and B. Mock addressed this question in the paper “College Basketball Upsets: Will a 16-Seed Ever Beat a 1-Seed?” (Chance, Vol. 11(1), pp. 27–31). They obtained the difference between the actual margin of victory and the point spread, called the point-spread error, for 2109 college basketball games. The
a. If, on average, the oddsmakers are estimating correctly, what is the (population) mean point-spread error?
b. Use the data to decide, at the 5% significance level, whether the (population) mean point-spread error differs from 0.
c. Interpret your answer in part (b).
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