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 158 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	17	10	12	19	9	10	10	12	12	18	17	12

Answer 1

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

H1: Atleast one of the month has different number of fatal accidents

Under H0, the expected number of fatal accident in each month is E =(17+10+....17+12)/12 = 158/12 =13.17

The calculations for Chi square test statistic is

Month	O	E	(O-E)^2/E
Jan	17	13.17	1.114
Feb	10	13.17	0.763
Mar	12	13.17	0.104
Apr	19	13.17	2.581
May	9	13.17	1.320
Jun	10	13.17	0.763
Jul	10	13.17	0.763
Aug	12	13.17	0.104
Sep	12	13.17	0.104
Oct	18	13.17	1.771
Nov	17	13.17	1.114
Dec	12	13.17	0.104
Total	158		10.605

The test statistic is

df = n-1= 11

Signiifcance level = 0.05

At 5% Significance level, the critical value of Chi square is 19.675

Since chi square calculated is less than chi square tabulated, Fail to REject the null hypothesis

Hence, there is not  enough evidence to reject the highway department executive's claim about the distribution of fatal accidents between each month.