Question

Many track runners believe that they have a better chance of winning if they start in the inside lane that is closest to the field. For the data below, the lane closest to the field is Lane 1, the next lane is Lane 2, and so on until the outermost lane, Lane 6. The data lists the number of wins for track runners in the different starting positions. Test the claim that the number of wins is uniformly distributed across the different starting positions. The results are based on 240 wins. Identify the claim, state the null and alternative hypotheses, find the critical value, find the standardized test statistic, make a decision on the null hypothesis (you may use a P-Value instead of the standardized test statistic), write an interpretation statement on the decision. Assuming a .05 significance level.

Starting Position		1	2	3	4	5	6
Number of Wins		33	45	36	44	50 32

Answer 1

Hypotheses are:

H0: The number of wins is uniformly distributed across the different starting positions.

Ha: The number of wins is not uniformly distributed across the different starting positions.

The sum of observed frequencies is 240 so expected frequency at each position is

Following table shows the calculations for chi square test statistics:

O	E	(O-E)^2/E
33	40	1.225
45	40	0.625
36	40	0.4
44	40	0.4
50	40	2.5
32	40	1.6
Total		6.75

The test statistics is

Degree of freedom:

df = 6-1 = 5

The p-value using excel function "=CHIDIST(6.75,5)" is 0.2399.

Since p-value is greater than 0.05 we fail to reject the null hypothesis. There is evidence to support the claim that the number of wins is uniformly distributed across the different starting positions.