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 109109 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	88	77	66	66	88	1010	66	1818	1111	66	66	1717

Step 1 of 10: State the null and alternative hypothesis.
H0: number or fatal accidents does not vary from month to month Ha: number or fatal accidents does vary from month to month
OR
H0:number or fatal accidents does vary from month to month, Ha:number or fatal accidents does not vary from month to month

Step 2 of 10: What does the null hypothesis indicate about the proportions of fatal accidents during each month?
Proportions of fatal accidents during each month are all thought to be equal
OR
Proportions of fatal accidents during each month are different for each category (and equal to previously accepted values)

Step 3 of 10: State the null and alternative hypothesis in terms of the expected proportions for each category.
H0: Pi= _______ Ha: there is some difference amongst the proportions

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 September. 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 0.10.1 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 0.10.1 level of significance.
Fail to reject null hypothesis OR Reject null hypothesis

Step 10 of 10: State the conclusion of the hypothesis test at the 0.10.1 level of significance.
There is not enough evidence to reject the claim that the number of fatal accidents does not vary from month to month OR there is enough evidence to reject the claim that the number of fatal accidents does NOT vary from month to month

Answer 1

applying chi square goodness of fit test:

	relative	observed	Expected	residual	Chi square
category	frequency(p)	Oi	Ei=total*p	R2i=(Oi-Ei)/√Ei	R2i=(Oi-Ei)2/Ei
Jan	1/12	8	9.08	-0.36	0.129
Feb	1/12	7	9.08	-0.69	0.478
Mar	1/12	6	9.08	-1.02	1.047
Apr	1/12	6	9.08	-1.02	1.047
May	1/12	8	9.08	-0.36	0.129
Jun	1/12	10	9.08	0.30	0.093
Jul	1/12	6	9.08	-1.02	1.047
Aug	1/12	18	9.08	2.96	8.753
Sep	1/12	11	9.08	0.64	0.404
Oct	1/12	6	9.08	-1.02	1.047
Nov	1/12	6	9.08	-1.02	1.047
Dec	1/12	17	9.08	2.63	6.900
total	1.000	109	109		22.1193
test statistic X2 =		22.119

step 1:

H0: number or fatal accidents does not vary from month to month Ha: number or fatal accidents does vary from month to month

step 2:

Proportions of fatal accidents during each month are all thought to be equal

step 3:

H0: Pi =1/12

step 4:

expected value =9.08

Step 5 of 10

expected value =9.08

step 6:

test statistic X2 =

22.119

step 7:

degree of freedom =categories-1=

11

step 8:

for 0.1 level and 11 df :crtiical value X2 =

17.275

step 9:

reject the null hypothesis

step 10)

there is enough evidence to reject the claim that the number of fatal accidents does NOT vary from month to month