Question

A highway department executive claims that the number of fatal accidents which occur in her state does not vary from month to month. The results of a study of 171 fatal accidents were recorded. Is there enough evidence to reject the highway department executive's claim about the distribution of fatal accidents between each month?

Month	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec
Fatal Accidents	22	8	8	17	8	10	23	11	13	13	20	18

Step 1 of 10:

State the null and alternative hypothesis.

Step 2 of 10:

What does the null hypothesis indicate about the proportions of fatal accidents during each month?

Step 3 of 10:

State the null and alternative hypothesis in terms of the expected proportions for each category.

Step 4 of 10:

Find the expected value for the number of fatal accidents that occurred in January. Round your answer to two decimal places.

Step 5 of 10:

Find the expected value for the number of fatal accidents that occurred in May. Round your answer to two decimal places

Step 6 of 10:

Find the value of the test statistic. Round your answer to three decimal places.

Step 7 of 10:

Find the degrees of freedom associated with the test statistic for this problem.

Step 8 of 10:

Find the critical value of the test at the 0.005 level of significance. Round your answer to three decimal places.

Step 9 of 10:

Make the decision to reject or fail to reject the null hypothesis at the 0.005 level of significance.

Step 10 of 10:

State the conclusion of the hypothesis test at the 0.005 level of significance.

Answer 1

Step 1

The null and alternative hypothesis

H0:  The distribution of fatal accidents between each month is Uniform.

H1:  The distribution of fatal accidents between each month is not Uniform.

Step 2

The null hypothesis indicat equal proportions of fatal accidents during each month.

Step 3

The null hypothesis Ho : E= 14.25

Alternative hypothesis H1 : E 14.25

Step 4

The expected value for the number of fatal accidents that occurred in January =14.25

Step 5

The expected value for the number of fatal accidents that occurred in May =14.25

Step 6

Calculation for test statistic

Month	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec	total
Fatal Accidents (O)	22	8	8	17	8	10	23	11	13	13	20	18	171
Expected Fre  ( E )	14.25	14.25	14.25	14.25	14.25	14.25	14.25	14.25	14.25	14.25	14.25	14.25	171
O-E	7.75	-6.25	-6.25	2.75	-6.25	-4.25	8.75	-3.25	-1.25	-1.25	5.75	3.75	0
(O-E)2/ E	4.215	2.741	2.741	0.531	2.741	1.268	5.373	0.741	0.11	0.11	2.32	0.987	23.877
E= 171/12 =14.25

Chi Square test statistics = 23.877

Step 7

The degrees of freedom associated with the test statistic for this problem is (12-1)=11

Step 8

The critical value of the test at the 0.005 level of significance = 26.757

Step 9

Decision: Chi Square test statistics (23.877 )< 26.757

Fail to reject the null hypothesis at the 0.005 level of significance

Step 10

Conclusion:

We conclude that the distribution of fatal accidents between each month is Uniform at the 0.005 level of significance.