In Exercise?, ?conduct the hypothesis test and provide the test statistic, critical value, and/or P-value, and state the conclusion. Kentucky Derby? The table below lists the frequency of wins for different post positions in the Kentucky Derby horse race (current as of this writing). A post position of 1 is closest to the inside rail, so that horse has the shortest distance to run. (Because the number of horses varies from year to year, only the first 10 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. Based on the result, should bettors consider the post position of a horse racing in the Kentucky Derby? P o s t P o s i t i o n W i n s

Solution 13BSC P o s t P o 1 1 2 3 4 5 6 7 8 9 s 0 i t i o n W i 1 1 1 1 1 1 1 7 8 5 n 9 4 1 5 4 2 1 s Step 1 By using = 0.05 significance level to test the claim that the likelihood of winning is the same for the different post positions. Expected frequency = 19 + 14 + . .= 11.61 10 The results are listed in the following table. Post position 11. 1 19 7.4 54.76 4.721 6 11. 2 14 2.4 5.76 0.497 6 11. 3 11 -0.6 0.36 0.031 6 11. 4 15 3.4 11.56 0.997 6 5 14 11. 2.4 5.76 0.497 6 11. 6 7 -4.6 21.16 1.824 6 11. 7 8 -3.6 12.96 1.117 6 11. 8 12 0.4 0.16 0.014 6 11. 9 5 -6.6 43.56 3.755 6 11. 10 11 -0.6 0.36 0.031 6 Total 116 116 13.483 Expected frequency = 11.6 is same for all categories. The Test Statistic here is 2 (Oi i ) = E = 13.483 i Where O iObserved frequency Ei= Expected frequency