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 160160 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   Fatal Accidents
Jan   11
Feb   8
Mar   18
Apr   14
May   11
Jun   11
Jul   13
Aug   16
Sep   13
Oct   13
Nov   21
Dec   11

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 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 July. 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 0.050.05 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 0.050.05 level of significance.

Step 10 of 10: State the conclusion of the hypothesis test at the 0.050.05 level of significance. Is there enough evidence?

Answer 1

step 1:
H0: the number of fatal accidents which occur in her state does not vary from month to month
H1: the number of fatal accidents which occur in her state vary from month to month

Step 2: H0: the proportions of fatal accidents during each month is same

Step 3: H1: the proportions of fatal accidents during each month is different

step 4: Expected valueof January is 160/12 = 13.33

Step 5: Expected valueof July is 160/12 = 13.33

Step 6: From the given data

	Observed	Expected
Month	Freq (Oi)	Freq Ei	(Oi-Ei)^2 /Ei
Jan	11	13.3333	0.408333
Feb	8	13.3333	2.133333
Mar	18	13.3333	1.633333
Apr	14	13.3333	0.033333
May	11	13.3333	0.408333
Jun	11	13.3333	0.408333
Jul	13	13.3333	0.008333
Aug	16	13.3333	0.533333
Sep	13	13.3333	0.008333
Oct	13	13.3333	0.008333
Nov	21	13.3333	4.408333
Dec	11	13.3333	0.408333
Total:	160	160	10.400000

Test Statistic, X^2: 10.400

Step 7: Degrees of freedom = 12-1 = 11

Step 8:  Critical X^2: 19.675

Step 9: Since Chi-square value < Chi-square critical value so we accept H0

Step 10: Thus we conclude that the number of fatal accidents which occur in her state does not vary from month to month i.e. the proportions of fatal accidents during each month is same