A sports statistician is interested in determining if there is a relationship between the number of home team and visiting team losses and different sports. A random sample of 526 games is selected and the results are given below. Test the claim that the number of home and visiting losses is independent of the sport. Use alpha = 0.01
Football Basketball Soccer Baseball
Home team losses 39 156 25 83
Visiting team losses 31 98 19 75
Please see the attachments.
The null hypothesis tested is
H0: The number of home and visiting losses is independent of the sport.
The alternative hypothesis is
H1: The number of home and visiting losses depends on sport.
The test statistic used is where O is the observed frequency and E is the expected frequency.
The Expected frequencies are given below. They are calculated using the formula , ,where Ri , ith row total, Cj jth column total and G is the grand Total.
Test statistic, ...
The solution provides step by step method for the calculation of chi square test for association. Formula for the calculation and Interpretations of the results are also included. Interactive excel sheet is included. The user can edit the inputs and obtain the complete results for a new set of data.