Question

The accompanying table summarizes successes and failures when subjects used different methods when trying to stop smoking. The determination of smoking or not smoking was made five months after the treatment was begun. If we test the claim that success is independent of the method​ used, the technology provides a​ P-value of 0.005 ​(rounded). What does the​ P-value tell us about that​ claim?

	Nicotine Gum	Nicotine Patch	Nicotine Inhaler
Smoking	187	266	87
Not Smoking	58	64	44

Answer 1

Ans:

Chi square test for independence:

	Observed(fo)
	Nicotine Gum	Nicotine Patch	Nicotine inhaler	Total
Smoking	187	266	87	540
Not Smoking	58	64	44	166
Total	245	330	131	706
	Expected(fe)
	Nicotine Gum	Nicotine Patch	Nicotine inhaler	Total
Smoking	187.39	252.41	100.20	540
Not Smoking	57.61	77.59	30.80	166
Total	245	330	131	706
	Chi square=(fo-fe)^2/fe
	Nicotine Gum	Nicotine Patch	Nicotine inhaler	Total
Smoking	0.00	0.73	1.74	2.47
Not Smoking	0.00	2.38	5.66	8.04
Total	0.00	3.11	7.39	10.51

Chi square test statistic=10.51

df=(2-1)*(3-1)=2
p-value=CHIDIST(10.51,2)=0.0052

Reject the null hypothesis(as small p-value provides strong evidence against null hypothesis)

There is sufficient evidence to conclude that success is not independent of the method​ used.