Question

In: Statistics and Probability

A highway department executive claims that the number of fatal accidents which occur in her state...

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 160160 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   11
Feb   8
Mar   18
Apr   14
May   11
Jun   11
Jul   13
Aug   16
Sep   13
Oct   13
Nov   21
Dec   11

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 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 July. 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 0.050.05 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 0.050.05 level of significance.

Step 10 of 10: State the conclusion of the hypothesis test at the 0.050.05 level of significance. Is there enough evidence?

Solutions

Expert Solution

step 1:
H0: the number of fatal accidents which occur in her state does not vary from month to month
H1: the number of fatal accidents which occur in her state vary from month to month

Step 2: H0: the proportions of fatal accidents during each month is same

Step 3: H1: the proportions of fatal accidents during each month is different

step 4: Expected valueof January is 160/12 = 13.33

Step 5: Expected valueof July is 160/12 = 13.33

Step 6: From the given data

Observed Expected
Month Freq (Oi) Freq Ei (Oi-Ei)^2 /Ei
Jan 11 13.3333 0.408333
Feb 8 13.3333 2.133333
Mar 18 13.3333 1.633333
Apr 14 13.3333 0.033333
May 11 13.3333 0.408333
Jun 11 13.3333 0.408333
Jul 13 13.3333 0.008333
Aug 16 13.3333 0.533333
Sep 13 13.3333 0.008333
Oct 13 13.3333 0.008333
Nov 21 13.3333 4.408333
Dec 11 13.3333 0.408333
Total: 160 160 10.400000

Test Statistic, X^2: 10.400

Step 7: Degrees of freedom = 12-1 = 11

Step 8:  Critical X^2: 19.675

Step 9: Since Chi-square value < Chi-square critical value so we accept H0

Step 10: Thus we conclude that the number of fatal accidents which occur in her state does not vary from month to month i.e. the proportions of fatal accidents during each month is same


Related Solutions

A highway department executive claims that the number of fatal accidents which occur in her state...
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...
A highway department executive claims that the number of fatal accidents which occur in her state...
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 171 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 22 8 8 17 8 10 23 11 13 13 20...
a highway department executive claims that the number of fatal accidents which occur in her state...
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 180 fatal accidents were recorded. is there enough evidence to reject the highway department executives 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 13 14 9 18 14 11 11 16 22 16...
A highway department executive claims that the number of fatal accidents which occur in her state...
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 161161 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 16 11 19 11 10 13 13 10 13 16 18...
A highway department executive claims that the number of fatal accidents which occur in her state...
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 162 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-19 Feb-8 Mar-21 Apr-13 May-10 Jun-18 Jul-10 Aug-14 Sept-13 Oct-8 Nov-10 Dec-18. Step 1 of 10: State the null and alternative hypothesis. Step...
A highway department executive claims that the number of fatal accidents which occur in her state...
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 161 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 16 8 10 13 13 11 16 16 13 13 18...
A highway department executive claims that the number of fatal accidents which occur in her state...
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...
A highway department executive claims that the number of fatal accidents which occur in her state...
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...
A highway department executive claims that the number of fatal accidents which occur in her state...
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 159 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? 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 highway department executive claims that the number of fatal accidents which occur in her state...
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 170170 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 1515 1010 1212 99 1515 2020 2020 2222 99 1414 1010...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT