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 140 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 8 15 9 8 13 6 17 15 10 9 18 12

Answer 1

There is enough evidence to reject the highway department executive's claim about the distribution of fatal accidents between each month, as the Variance is 14 and the Standard Deviation = 4 approximately.

There is a high degree of variability in the mean of the population as explained by the Variance and the Standard Deviation.

Explanation:

Month No. of Mean Squared

Fatal Accidents Deviation Difference

Jan 8 -4 16

Feb 15 3 9

Mar 9 -3 9

Apr 8 -4 16

May 13 1 1

Jun 6 -6 36

Jul 17 5 25

Aug 15 3 9

Sep 10 -2 4

Oct 9 -3 9

Nov 18 6 36

Dec 12 0 0

Total 140 170

Mean = 140/12 = 12 Mean of squared deviation (Variance) = 170/12 = 14.16667

Standard deviation = square root of variance = 3.76386 = 4

The fatal accidents' Variance is a measure of how spread out the fatal accident data set is. It is calculated as the average squared deviation of the number of each month's accident from the mean of the fatal accident data set. It also shows how variable the data varies from the mean of approximately 12.

The fatal accidents' Standard Deviation is the square root of the variance, and a useful measure of variability when the distribution is normal or approximately normal.