In: Statistics and Probability
A sports researcher is interested in determining if there is a relationship between the number of home team and visiting team wins and different sports. A random sample of 633 games is selected and the results are given below. Conduct test of hypothesis to test the claim that the number of home team and visiting team wins is independent of the sport. Use a=0.05.
Football | BasketBall | Soccer | Baseball | |
Hometeam Wins | 89 | 165 | 91 | 49 |
Visiting Team Wins | 60 | 89 | 52 | 38 |
Please use SPSS if available to solve
Null hypothesis ( H0 ) : the number of home team and visiting team wins is independent of the sport
Alternative hypothesis ( Ha ) : the number of home team and visiting team wins is dependent of the sport
:Observed Frequencies
B1 | B2 | B3 | B4 | Total | |
A1 | 89 | 165 | 91 | 49 | 394 |
A2 | 60 | 89 | 52 | 38 | 239 |
Total | 149 | 254 | 143 | 87 | 633 |
Expected Frequencies
B1 | B2 | B3 | B4 | Total | |
A1 | 92.7425 | 158.0979 | 89.0079 | 54.1517 | 394 |
A2 | 56.2575 | 95.9021 | 53.9921 | 32.8483 | 239 |
Total | 149 | 254 | 143 | 87 | 633 |
Compute Chi-square
Test statistic = 2.614
Compute the degrees of freedom (df).
df=(2-1)⋅(4-1)=3
for 3 df, p(χ2≥2.6142)=0.455
Decision :
Since the p-value(0.455) > α(0.05) (one-tailed test), we can't reject the null hypothesis H0.
Conclusion :
At a = 0.05 L.O.S there is enough evidence to claim that the number of home team and visiting team wins is independent of the sport.