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 158 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 17 10 12 19 9 10 10 12 12 18 17 12

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 April. 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 0.1 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 0.1 level of significance. Step 10 of 10: State the conclusion of the hypothesis test at the 0.1 level of significance.

Answer 1

Step 1 of 10: Ho :number of fatal accidents which occur in her state are uniformly distributed or p=1/12 for each month

alternate hypothesis:Ha: number of fatal accidents which occur in her state are not uniformly distributed or for at least one month p is not equal to 1/12

Step 2 of 10: p=1/12

Step 3 of 10: p_Jan =P_feb =....=1/12

step 4:  expected value for the number of fatal accidents that occurred in January=158/12 =13.17

Step 5 of 10:expected value for the number of fatal accidents that occurred in  April=13.17

Step 6:

	relative	observed	Expected	residual	Chi square
category	frequency	Oi	Ei=total*p	R2i=(Oi-Ei)/√Ei	R2i=(Oi-Ei)2/Ei
1	1/12	17.000	13.167	1.06	1.116
2	1/12	10.000	13.167	-0.87	0.762
3	1/12	12.000	13.167	-0.32	0.103
4	1/12	19.000	13.167	1.61	2.584
5	1/12	9.000	13.167	-1.15	1.319
6	1/12	10.000	13.167	-0.87	0.762
7	1/12	10.000	13.167	-0.87	0.762
8	1/12	12.000	13.167	-0.32	0.103
9	1/12	12.000	13.167	-0.32	0.103
10	1/12	18.000	13.167	1.33	1.774
11	1/12	17.000	13.167	1.06	1.116
12	1/12	12.000	13.167	-0.32	0.103
total	1.000	158	158		10.6076

test statisitc =10.608

  Step 7:

degree of freedom =categories-1=

11

  Step 8:

for 0.1 level and 11 degree of freedom :rejection region =

17.275

  Step 9 :fail to rject

step 10) there is not sufficient evidence ,,,,,,,,