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 148 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	8	10	24	11	11	14	10	8	7	16	10	19

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 November. 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 0.05 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 0.05 level of significance.

Step 10 of 10:

State the conclusion of the hypothesis test at the 0.05 level of significance.

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	0.0833	8.00	12.33	-1.23	1.523
Feb	0.0833	10.00	12.33	-0.66	0.441
Mar	0.0833	24.00	12.33	3.32	11.036
Apr	0.0833	11.00	12.33	-0.38	0.144
May	0.0833	11.00	12.33	-0.38	0.144
Jun	0.0833	14.00	12.33	0.47	0.225
Jul	0.0833	10.00	12.33	-0.66	0.441
Aug	0.0833	8.00	12.33	-1.23	1.523
Sep	0.0833	7.00	12.33	-1.52	2.306
Oct	0.0833	16.00	12.33	1.04	1.090
Nov	0.0833	10.00	12.33	-0.66	0.441
Dec	0.0833	19.00	12.33	1.90	3.604
total	1.000	148	148		22.9189
test statistic X2 =		22.9189

Step 1 of 10: : Null hypothesis: Ho  fatal accidents are uniformly distributed in each month

Alternate hypothesis: Ha: fatal accidents are not uniformly distributed in each month

step 2: proportions of fatal accidents during each month are equal

step 3: expected proportion =1/12

step 4:

expected value for the number of fatal accidents that occurred in January. =np=12.33

step 5: expected value =12.33

Step 6 of 10: value of the test statistic =22.919

step 7:

degree of freedom =categories-1=

11

step 8:

for 0.05 level and 11 df :crtiical value X2 =

19.675

Step 9 of 10:

reject the null

step 10:

we have enough evidence to conclude that ..............