Question

To test whether the enactment of seatbelt legislation had any association with injuries to vehicle users, a random sample of 7676 individuals taken over a two-year period (one year prior legislation and one year post legislation) was used. The results are detailed below.

	Post Legislation	Prior Legislation	Total
No Injury	1320	5430	6750
Minimal Injury	70	552	622
Major Injury	32	224	256
Fatal Injury	10	38	48
Total	1432	6244	7676

Please write a summary statement for this hypothesis test.

Answer 1

Hypotheses are:

H0: The enactment of seat-belt legislation had no association with injuries to vehicle users.

Ha: The enactment of seat-belt legislation had an association with injuries to vehicle users.

Expected frequencies will be calculated as follows:

Following table shows the expected frequencies;

	Post Legislation	Prior legislation	Total
No Injury	1259.25	5490.75	6750
Minimal Injury	116.038	505.962	622
Major Injury	47.758	208.242	256
Fatal Injury	8.955	39.045	48
Total	1432	6244	7676

Following table shows the calculations for chi square test statistics:

O	E	(O-E)^2/E
1320	1259.25	2.930762359
70	116.038	18.26554615
32	47.758	5.199433896
10	8.955	0.12194584
5430	5490.75	0.672141784
552	505.962	4.189044719
224	208.242	1.19243267
38	39.045	0.02796837
Total		32.59927579

The test statistics is:

Degree of freedom: df =( number of rows -1)*(number of columns-1) = (4-1)*(2-1)=3

The p-value using excel function "=Chidist(32.599,3)" is: 0.0000

Since p-value is less than 0.05 so we reject the null hypothesis. That is there is evidence to conclude that  the enactment of seatbelt legislation had any association with injuries to vehicle users.