Question

In: Statistics and Probability

A sports researcher is interested in determining if there is a relationship between the number of...

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

Solutions

Expert Solution

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.


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