Question

A study of seat belt users and nonusers yielded the randomly selected sample data summarized in the accompanying table. Use a 0.05 significance level to test the claim that the amount of smoking is independent of seat belt use. A plausible theory is that people who smoke are less concerned about their health and safety and are therefore less inclined to wear seat belts. Is this theory supported by the sample​ data?

data set below

Wear seat belts don't wear seat belts	number of cigarettes smoked per day
	0		1-14	5-34		35 and over
	180		10	37		5
	144		19	45		13

Determine the test statistic.

​(Round to three decimal places as​ needed.)

Determine the​ P-value of the test statistic.

(Round to three decimal places as​ needed.)

Use a 0.05 significance level to test the claim that the amount of smoking is independent of seat belt use. A plausible theory is that people who smoke are less concerned about their health and safety and are therefore less inclined to wear seat belts. Is this theory supported by the sample​ data?

A.There is sufficient evidence to reject the claim that the amount of smoking is independent of seat belt use. The theory is supported by the sample data.

B. There is not sufficient evidence to reject the claim that heavy smokers are less likely than​ non-smokers to wear a seat belt. The theory is not supported by the sample data.

C. There is sufficient evidence to reject the claim that heavy smokers are less likely than​ non-smokers to wear a seat belt. The theory is not supported by the sample data.

D. There is not sufficient evidence to reject the claim that the amount of smoking is independent of seat belt use. The theory is supported by the sample data.

Answer 1

Applying chi square test of independence:

Expected	Ei=row total*column total/grand total	defective	acceptable	acceptable	acceptable	Total
	waer	165.930	14.852	41.996	9.219	232
	do not wear	158.066	14.148	40.004	8.781	221
	total	324	29	82	18	453
chi square    χ2	=(Oi-Ei)2/Ei	defective	acceptable	acceptable	acceptable	Total
	waer	1.193	1.585	0.594	1.930	5.3029
	do not wear	1.252	1.6641	0.6238	2.0266	5.5662
	total	2.4448	3.2492	1.2181	3.9570	10.869
test statistic X2 =		10.869
p value =		0.012

since p value <0.05

A.There is sufficient evidence to reject the claim that the amount of smoking is independent of seat belt use. The theory is supported by the sample data.