·The authors of the Article \"Predicting Professional Sports Game Outcomes from

Question

·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 seftled until the lasi quairter, whereas baseball games are overby the seventh inning and hockey. Data was collected for 189'basketball games, 2 baseball games, 80 hockey games, and 93 football games. The games ahalyzed were sampled randomly from áll games played during the 1990 season for baseball and football and for the 1990-1991 season for baskeiball and', hockeý. For each- gamie, the late-game leader was deter- mined, and then it was noted whether the late-gaie leader actually ended up winning the game. The resulting data is summarized in yie accompanying table. also considered football Late-Game Leader Loses Sport Basketball. 15 Footba

Explanation / Answer

here null hypothesis: Ho: probability of late game wins is indepednent of type of sport.

alternate hypothesis:Ha: probability of late game wins is depednent of type of sport.

applying chi square test of independence on above:

degree of freedom =(number of rows-1)*(number of columns-1)=(4-1)*(2-1)=3

for 3 degrees of freedom and abvoe test stat 10.518 ;pvalue =0.0146

as p value is less then 0.05 level; we reject null hypothesis and conclude that proportion of late game leader wins is not same for all 4 sports.

Observed O late game wins late game loses Total Basketball 150 39 189 Baseball 86 6 92 Hockey 65 15 80 Football 72 21 93 Total 373 81 454 Expected E=rowtotal*column total/grand total late game wins late game loses Total Basketball 155.28 33.72 189 Baseball 75.59 16.41 92 Hockey 65.73 14.27 80 Football 76.41 16.59 93 Total 373 81 454 chi square =(O-E)^2/E late game wins late game loses Total Basketball 0.1795 0.8267 1.006 Baseball 1.4348 6.6073 8.042 Hockey 0.0080 0.0370 0.045 Football 0.2542 1.1708 1.425 Total 1.877 8.642 10.518

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