The table below lists the frequency of wins for different post positions in the

Question

The table below lists the frequency of wins for different post positions in the Kentucky Derby horse race. A post position of 1 is closest to the inside rail, so that hors has the shortest distance to run. (Because the number of horses varies from year to year, only the first ten post positions are included.) Use a 0.05 significance level to test the claim that the likelihood of winning is the same for the different post positions. Base on the result, should bettors consider the post positon of a horse racing in the Kentucky Derby?

Ho:

Ha:

P-value:

Conclusion:

Should bettors consider the post positon of a horse racing in the Kentucky Derby?

Post positions 1 2 3 4 5 6 7 8 9 Wins 19 14 11 14 14 7 8 11 5

Explanation / Answer

Here,

Ho: All horses are equally likely to win.
Ha: Horses are not equally likely to win.

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There are 104 results here, so we expect each of them to get 104/10 = 10.4 wins.

Doing an observed/expected value table,          

  

Using chi^2 = Sum[(O - E)^2/E],          
          
chi^2 =    23.88461538      
          
As df = a - 1,           
          
a =    10      
df = a - 1 =    9      
          
Also, the p value is, by technology,          
          
p =    0.004487508   [ANSWER, P VALUE]

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As P < 0.05, we   REJECT THE NULL HYPOTHESIS.      
          
Thus, there is significant evidence that horses are not equally likely to win. Yes, bettors should consider the post positon of a horse racing in the Kentucky Derby. [COCNLUSION]

O E (O - E)^2/E 19 10.4 7.111538 14 10.4 1.246154 11 10.4 0.034615 14 10.4 1.246154 14 10.4 1.246154 7 10.4 1.111538 8 10.4 0.553846 11 10.4 0.034615 5 10.4 2.803846 1 10.4 8.496154

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