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 180 fatal accidents were recorded. is there enough evidence to reject the highway department executives 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	11	13	14	9	18	14	11	11	16	22	16	25

Step 1: state the null and alternative null hypothesis

Step 2: What does the null hypothesis indicate about the proportions of fatal accidents during each month

Step 3: State the null and alternative hypothesis in terms of the expected proportions of each category

Ho:pi=

Step 4: Find the expected value for the number of fatal accidents that occurred in January. round to two decimal places

Step 5: FInd the expected value for the number of fatal accidents that occurred in November. round to two decimal places

Step 6: find the value of the test statistic. round to three decimal places.

Step 7: Find the degree of freedom adssociated with the test statiscctic for this problem

Step 8: Find the critical value of the test at the 0.025 level of significance. round to three decimal places.

Step 9: Make the decision to reject or fail to reject the null hypothesis at the 0.025 level of significance

Step 10: State the conclusion of the hypothesis test at the 0.025 level of significance.

There is or is not enough evidence to reject the claim the number of fatall accidents from month to month

Answer 1

step 1:)

Null hypothesis:Ho: Number of accidents are uniformly distributed across months

Alternate hypothesis: Ho: Number of accidents are not uniformly distributed across months

step 2: null hypothesis indicate that proportion of fatal accidents are equal in each month

step 3 Ho: pi=1/12

step 4: expected value for the number of fatal accidents that occurred in January =np=180*1/12

=15

step 5: expected value for the number of fatal accidents that occurred in November.

=180*1/12 =15

Step 6:

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	11.000	15.000	-1.03	1.067
Feb	1/12	13.000	15.000	-0.52	0.267
Mar	1/12	14.000	15.000	-0.26	0.067
Apr	1/12	9.000	15.000	-1.55	2.400
May	1/12	18.000	15.000	0.77	0.600
Jun	1/12	14.000	15.000	-0.26	0.067
Jul	1/12	11.000	15.000	-1.03	1.067
Aug	1/12	11.000	15.000	-1.03	1.067
Sep	1/12	16.000	15.000	0.26	0.067
Oct	1/12	22.000	15.000	1.81	3.267
Nov	1/12	16.000	15.000	0.26	0.067
Dec	1/12	25.000	15.000	2.58	6.667
total	1.000	180	180		16.6667
test statistic X2 =		16.667

Step 7

degree of freedom =categories-1=

11

step 8:

for 0.025 level and 11 df :crtiical value X2 =

21.920

Step 9: fail to reject the null hypothesis

step 10: There is not enough evidence to reject the claim the number of fatall accidents from month to month