Chapter 14, Problem 40SE

The authors of the article “Predicting Professional Sports Game Outcomes from Intermediate Game Scores” (Chance, 1992: 18–22) used a chi-squared test to determine whether there was any merit to the idea that basketball games are not settled until the last quarter, whereas baseball games are over by the seventh inning. They also considered football and hockey. Data was collected for 189 basketball games, 92 baseball games, 80 hockey games, and 93 football games. The games analyzed were sampled randomly from all games played during the 1990 season for baseball and football and for the 1990–1991 season for basketball and hockey. For each game, the late-game leader was determined, and then it was noted whether the late-game leader actually ended up winning the game. The resulting data is summarized in the accompanying table.

Sport Basketball	Late-Game Leader Wins 150	Late-Game Leader Loses 39
Baseball	86	6
Hockey	65	15
Football	72	21

The authors state that “Late-game leader is defined as the team that is ahead after three quarters in basketball and football, two periods in hockey, and seven innings in baseball. The chi-square value on three degrees of freedom is 10.52 (P < .015).”

a. State the relevant hypotheses and reach a conclusion using α = .05.

b. Do you think that your conclusion in part (a) can be attributed to a single sport being an anomaly?