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 179 179 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-14 Feb-18 Mar-11 Apr-14 May-11 Jun-20 Jul-11 Aug-16 Sept-16 Oct-11 Nov-14 Dec- 23

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 April. 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 0.0250.025 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 0.0250.025 level of significance.

Step 10 of 10: State the conclusion of the hypothesis test at the 0.0250.025 level of significance.

Answer 1

Step 2 of 10: Let p indicate the proportion of fatal incidents that occur every month.

The null hypothesis suggests that the number of fatal incidents occurring every month doesn't vary i.e. for every month the number of fatal incidents lies inside a certain interval and hence can be called as not varying over the months.

Step 3 of 10: The Null Hypothesis

where 1, 2, 3 ......... 12 represent the twelve months of the year.

The alternate hypothesis

Step 4 of 10: Expected value for the number of fatal accidents occurring in January will be equal to the sample mean which is a point estimate of the population mean.

Step 5 of 10: Since the claim is that the number of fatal incidents doesn't vary over the months hence the expected value for the number of fatal accidents in April will also be equal to the sample mean which is a point estimate of the population mean.

Step 6 of 10: The value of the test statistics will be calculated for each of the months.

But before that we need to calculate the sample standard deviation for the number of fatal accidents occurring every month.

where is the sample mean of the no. of fatal accidents occurring every month.

Value of the test statistic

Step 7 of 10: The degree of freedom associated with the test statistics is equal to n-1 where n = 12.

Since, if we fix the no. of fatal accidents for 11 months then the no. of accidents for the 12th month gets fixed automatically. Hence the degree of freedom is equal to 11.

Step 8 of 10: Critical value for the test with a significance level of 0.025 and degree of freedom 11 can be calculated from the t table. The critical value is .

Step 9 of 10: The decision to reject or fail the null hypothesis at 0.025 significance level will be based on the fact that whether any of the calculated value of the test statistics lies outside the interval specified by the critical value of the test.

From the above-calculated values, we can observe that the value of the test statistics exceeds the interval for the critical value in case of 7 months among the 12 months. Hence, we reject the null hypothesis.

Step 10 of 10: To conclude, based on the hypothesis test, that if the number of fatal accidents lied in a certain interval as specified by the critical value of the test based on a significance level of 0.025, then we would have accepted the null hypothesis. But since 7 out of 12 months' data exceeds the limit for the critical value so we can easily reject the claim made by the executive. The number of fatal accidents varies a lot from month to month.

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