Question

It is believed that in horse races on a circular racetrack, the starting position has an impact on the chances of winning.
 The following table breaks down 200 winners by the number of their starting position

StartingPosition	1	2	3	4	5	6	7	8
Number of Wins	22	30	34	23	21	20	31	19

Test the null hypothesis "equal chances of winning" against the alternative
"the Starting position has an influence on the result ”  at the (significance)Niveau α = 0.05 using the 
Chi-square goodness of fit test

Please explain the steps for a good understand. Appreciate your HElp!

Answer 1

H₀: equal chances of winning and H₁: the Starting position has an influence on the result

Here we're going to use the chi-square goodness of fit test.

Here we're already given the observed values. The expected value is 25 for all.

The test statistic is given as:

, The test statistic follows a chi-square distribution with (8-1)=7 degree of freedom. Thus at level , the critical value is .

thus the test statistic is:

The obtained test statistic is less than the critical value thus we fail to reject the H₀.