Question

The table below lists the frequency of wins for different post positions in a horse race. 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​ race?

Post_Position   Wins
1   19
2   15
3   11
4   14
5   14
6   8
7   7
8   13
9   5
10   12

Determine the null and alternative hypotheses.

Upper H 0H0​:

▼

At least one post position has a different frequency of wins than the others.

Wins occur with all different frequency in the different post positions.

Wins occur with equal frequency in the different post positions.

At least one post positions have a different frequency of wins than the others.

Upper H 1H1​:

▼

At least one post positions have a different frequency of wins than the others.

At least one post position has a different frequency of wins than the others.

Wins occur with all different frequency in the different post positions.

Wins occur with equal frequency in the different post positions.

Calculate the test​ statistic,

chi squaredχ2.

chi squaredχ2equals=nothing

​(Round to three decimal places as​ needed.)

Calculate the​ P-value.

​P-valueequals=nothing

​(Round to four decimal places as​ needed.)

What is the conclusion for this hypothesis​ test?

A.

RejectReject

Upper H 0H0.

There is

sufficientsufficient

evidence to warrant rejection of the claim that the likelihood of winning is the same for the different post positions.

B.

Fail to rejectFail to reject

Upper H 0H0.

There is

sufficientsufficient

evidence to warrant rejection of the claim that the likelihood of winning is the same for the different post positions..

C.

Fail to rejectFail to reject

Upper H 0H0.

There is

insufficientinsufficient

evidence to warrant rejection of the claim that the likelihood of winning is the same for the different post positions.

D.

RejectReject

Upper H 0H0.

There is

insufficientinsufficient

evidence to warrant rejection of 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​ race?

NoNo

YesYes

Click to select your answer(s).

Answer 1

Category	Observed Frequency (O)	Expected Frequency (E)	(O-E)²/E
1	19	118 * 0.1 = 11.8	(19 - 11.8)²/11.8 = 4.3932
2	15	118 * 0.1 = 11.8	(15 - 11.8)²/11.8 = 0.8678
3	11	118 * 0.1 = 11.8	(11 - 11.8)²/11.8 = 0.0542
4	14	118 * 0.1 = 11.8	(14 - 11.8)²/11.8 = 0.4102
5	14	118 * 0.1 = 11.8	(14 - 11.8)²/11.8 = 0.4102
6	8	118 * 0.1 = 11.8	(8 - 11.8)²/11.8 = 1.2237
7	7	118 * 0.1 = 11.8	(7 - 11.8)²/11.8 = 1.9525
8	13	118 * 0.1 = 11.8	(13 - 11.8)²/11.8 = 0.122
9	5	118 * 0.1 = 11.8	(5 - 11.8)²/11.8 = 3.9186
10	12	118 * 0.1 = 11.8	(12 - 11.8)²/11.8 = 0.0034
Total	118	118	13.356

Null and alternative hypotheses.

H0​: Wins occur with equal frequency in the different post positions.

H1​: At least one post position has a different frequency of wins than the others.

Test statistic:

χ² = ∑ ((fo-fe)²/fe) = 13.356

df = n-1 = 9

p-value:

p-value = CHISQ.DIST.RT(13.3559, 9) = 0.1472

Conclusion:

Answer C. Fail to reject H0. There is insufficient evidence to warrant rejection of 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​ race?

No