Question

Below is a contingency table consisting of seat belt use and amount of smoking per day. Use a .05 significance level to test the claim that the amount of smoking is independent of seat belt use.

	Number of Cigarettes Smoked per Day
	0	1 – 14	15 – 34	35 and over
Wear Seat Belts	175	20	42	6
Don’t Wear Seat Belts	149	17	41	9

Test the claim using the critical value method (Check your answer with the p-value on the calculator).

Answer 1

Null hypothesis: Ho:  amount of smoking is independent of seat belt use.

Alternative hypothesis: Ha:  amount of smoking is dependent of seat belt use.

degree of freedom(df) =(rows-1)*(columns-1)=		3
for 3 df and 0.05 level , critical value       χ2=		7.815
Decision rule : reject Ho if value of test statistic X2>7.815

Expected	Ei=row total*column total/grand total	0 Cigrettes	1-14	15-34	35 and over	Total
	wear	171.53	19.59	43.94	7.94	243
	do not wear	152.47	17.41	39.06	7.06	216
	total	324	37	83	15	459
chi square    χ2	=(Oi-Ei)2/Ei	0 Cigrettes	1-14	15-34	35 and over	Total
	wear	0.070	0.009	0.086	0.475	0.6391
	do not wear	0.079	0.010	0.096	0.534	0.7190
	total	0.1492	0.0184	0.1822	1.0083	1.3582
test statistic X2 =		1.358

p value from excel:=chidist(1.358,3)=

0.7154

since test statistic does not falls in rejection region we fail to reject null hypothesis

we do not have have sufficient evidence to reject the claim that the amount of smoking is independent of seat belt use.