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 170 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 :

11 19 24 16 11 7 7 17 9 19 18 12

State the null and alternative hypothesis.

What does the null hypothesis indicate about the proportions of fatal accidents during each month?

State the null and alternative hypothesis in terms of the expected proportions for each category.

Find the value of the test statistic. Round your answer to three decimal places.

Find the degrees of freedom associated with the test statistic for this problem.

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

Make the decision to reject or fail to reject the null hypothesis at the 0.01 level of significance.

State the conclusion of the hypothesis test at the 0.01 level of significance.

Answer 1

we can quickly solve this in excel , please see the excel screenshots below

we assume that the numbers should be the same across the months

State the null and alternative hypothesis.

H0 :A highway department executive claims that the number of fatal accidents which occur in her state does not vary from month to month.
H1 : A highway department executive claims that the number of fatal accidents which occur in her state does vary from month to month.

What does the null hypothesis indicate about the proportions of fatal accidents during each month?

that they must remain the same across the months

State the null and alternative hypothesis in terms of the expected proportions for each category.

H0 :A highway department executive claims that the proportions of fatal accidents which occur in her state does not vary from month to month.
H1 : A highway department executive claims that the proportions of fatal accidents which occur in her state does vary from month to month.

Find the value of the test statistic. Round your answer to three decimal places.

we perform a chi sqaure test as shown below

df = n-1 = 11

as the p value is not less than 0.01 and is 0.0185 , hence we fail to reject the null hypothesis in favor of alternate hypothesis and conclude that hat the proportions of fatal accidents which occur in her state does not vary from month to month.