Question

The following table is taken from the publication 1992 Uniform Crime Reports for the United States. It gives the distribution by region for 1992 motor vehicle thefts. (A sample of 100 records was selected from each region.).Test the null hypothesis that there is no relationship between region of the country, and type of vehicle stolen. Use the .05 significance level

Region	Cars	Other
NE	85	15
Mid W	80	20
S	65	35
W	60	40

Answer 1

null hypothesis:Ho: there is no relationship between region of the country, and type of vehicle stolen.

Alternate hypothesis:Ho: there is a significant relationship between region of the country, and type of vehicle stolen.

degree of freedom(df) =(rows-1)*(columns-1)=

3

for 3 df and 0.05 level of signifcance critical region       χ2=

7.815

Applying chi square test of independence:

Expected	Ei=row total*column total/grand total	Cars	Other	Total
	NE	72.50	27.50	100
	Mid W	72.50	27.50	100
	S	72.50	27.50	100
	W	72.50	27.50	100
	total	290	110	400
chi square    χ2	=(Oi-Ei)2/Ei	Cars	Other	Total
	NE	2.1552	5.6818	7.837
	Mid W	0.7759	2.0455	2.821
	S	0.7759	2.0455	2.821
	W	2.1552	5.6818	7.837
	total	5.862	15.455	21.3166

test statistic X² =21.317

as test statistic fall in rejection region ; we reject null hypothesis and conclude that there is a significant relationship between region of the country, and type of vehicle stolen.