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 160 160 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   23
Feb   10
Mar   10
Apr   12
May   19
Jun   10
Jul   14
Aug   8
Sep   7
Oct   21
Nov   16
Dec   10

Step 1: State the null and alternative 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 for each category.

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

Step 5: Find the expected value for the number of fatal accidents that occurred in July. Round your answer to two decimal places.

Step 6: Find the value of the test statistic and the degrees of freedom. Round your answer to three decimal places.

Step 7: Find the critical value of the test at the 0.01 level of significance. Round your answer to three decimal places.

Step 8: State the conclusion of the hypothesis test at the 0.01 level of significance.

I would like to see work if possible. thank you

Answer 1

Ans:

H_o:Each proportion is equal to 1/12

Ha:At least one proportion is different from 1/12

For each category,Expected proportion=1/12

For each category,Expected frequency=160/12=13.333

Month	fo	expected prop.	fe	(fo-fe)^2/fe
Jan	23	0.0833	13.33	7.008
Feb	10	0.0833	13.33	0.833
Mar	10	0.0833	13.33	0.833
Apr	12	0.0833	13.33	0.133
May	19	0.0833	13.33	2.408
Jun	10	0.0833	13.33	0.833
Jul	14	0.0833	13.33	0.033
Aug	8	0.0833	13.33	2.133
Sep	7	0.0833	13.33	3.008
Oct	21	0.0833	13.33	4.408
Nov	16	0.0833	13.33	0.533
Dec	10	0.0833	13.33	0.833
Total	160	1	160	23.000

Chi square test statistic=23.000

df=12-1=11

Critical chi square=CHIINV(0.01,11)=24.725

Fail to reject the null hypothesis.