Question

Post Position	1	2	3	4	5	6	7	8	9	10
Wins	19	14	11	15	15	7	8	12	5	11

The table below lists the frequency of wins for different post positions in the Kentucky Derby horse race.

Use a 0.05 significance level to test the claim that the likelihood of winning is the same for the different post positions.

What is the critical value (the X2 value)? [Round to the nearest thousandths place]

Answer 1

total frequency=   117
expected frequncy,E = expected proportions*total frequency  

observed frequencey, O	expected proportion	expected frequency,E	(O-E)		(O-E)²/E
19	0.100	11.70	7.30		4.555
14	0.100	11.70	2.30		0.452
11	0.100	11.70	-0.70		0.042
15	0.100	11.70	3.30		0.931
15	0.100	11.70	3.30		0.931
7	0.100	11.700	-4.70		1.888
8	0.100	11.700	-3.70		1.170
12	0.100	11.700	0.30		0.008
5	0.100	11.700	-6.70		3.837
11	0.100	11.700	-0.70		0.042

chi square test statistic,X² = Σ(O-E)²/E =   13.855              
                  
level of significance, α=   0.05              
Degree of freedom=k-1=   10   -   1   =   9
                                
Critical value =    16.919   [ Excel function: =chisq.inv.rt(α,df) ]          
Decision: test stat < critical  , Do not reject Ho