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 120120 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	1010	1212	77	1313	66	1010	1313	66	1010	1111	88	1414

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 August. 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 0.010.01 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 0.010.01 level of significance.

Step 10 of 10:

State the conclusion of the hypothesis test at the 0.010.01 level of significance.

Answer 1

Answer:

H0: the number of fatal accidents which occur in her state does not vary from month to month

H1: Atleast one of the month has different number of fatal accidents

proportion is same for all months

the expected number of fatal accident in each month is E =(10+12 +....8+14)/12 = 120 /12 =10
H0: expected proportion each month is 10/120
Ha: expected proportion for any month is different that 10/120

Month	Oi	Ei = 120/12	(Oi - Ei)^2/Ei
jan	10	10	0
feb	12	10	0.4
mar	7	10	0.9
apr	13	10	0.9
may	6	10	1.6
jun	10	10	0
jul	13	10	0.9
aug	6	10	1.6
sep	10	10	0
oct	11	10	0.1
nov	8	10	0.4
dec	14	10	1.6
Total	120		8.4

The test statistic is

= 8.4

df = n-1= 12 - 1 = 11

Signiifcance level = 0.01

At 1% Significance level, the critical value of Chi square is 24.725

Critical value = 24.725

Since chi square calculated is less than chi square tabulated, Fail to REject the null hypothesis

Hence, there is not  enough evidence to reject the highway department executive's claim about the distribution of fatal accidents between each month.

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