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 161 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	16	8	10	13	13	11	16	16	13	13	18	14

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 February. 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

null hypothesis: all proportion are equal

Alternate hypothesis: Not all proportion are equal

step 3:  Ho: pjan=pfeb=pmarch =.....p i=1/12

Ha: pj is not equal to 1/12

step4:

expected value for the number of fatal accidents that occurred in January =np=161*1/12= 13.4

5)

expected value for the number of fatal accidents that occurred in February =13.4

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
1	0.08	16.0	13.42	0.71	0.497
2	0.08	8.0	13.42	-1.48	2.187
3	0.08	10.0	13.42	-0.93	0.870
4	0.08	13.0	13.42	-0.11	0.013
5	0.08	13.0	13.42	-0.11	0.013
6	0.08	11.0	13.42	-0.66	0.435
7	0.08	16.0	13.42	0.71	0.497
8	0.08	16.0	13.42	0.71	0.497
9	0.08	13.0	13.42	-0.11	0.013
10	0.08	13.0	13.42	-0.11	0.013
11	0.08	18.0	13.42	1.25	1.566
12	0.08	14.0	13.42	0.16	0.025
total	1.000	161	161		6.6273
test statistic X2 =		6.627

Step 7 of 10:

degree of freedom =categories-1=

11

Step 8 of 10:

for 0.005 level and 11 df :crtiical value X2 =

26.757

Step 9 of 10:

fail to reject the null hypothesis

Step 10 of 10:

conclude that  number of fatal accidents which occur in her state does not vary from month to month.