In: Statistics and Probability
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?
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