Question

The paper “Cigarette Tar Yields in Relation to Mortality from Lung Cancer in the Cancer Prevention Study II Prospective Cohort “ (British Medical Journal [2004]: 72-79) included the accompanying data on the tar level of cigarettes smoked for a sample of male smokers who subsequently died of lung cancer.

Tar Level	Frequency
0-7mg	103
8-14 mg	378
15-21 mg	563
≥ 22 mg	150

Assume it is reasonable to regard the sample as representative of male smokers who die of lung cancer. Is there convincing evidence that the proportion of male smoker long cancer death is not the same for the four given tar level categories?

Answer 1

Null Hypothesis:Ho: proportion of male smoker long cancer death is the same for the four given tar level categories.

Alternate hypothesis:Ha: proportion of male smoker long cancer death is not the same for the four given tar level categories

degree of freedom =categories-1=

3

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

7.815

applying chi square goodness of fit test:

	relative	observed	Expected	residual	Chi square
category	frequency	Oi	Ei=total*p	R2i=(Oi-Ei)/√Ei	R2i=(Oi-Ei)2/Ei
0-7	0.250	103	298.50	-11.32	128.041
8-14	0.250	378	298.50	4.60	21.173
15-21	0.250	563	298.50	15.31	234.373
>=22	0.250	150	298.50	-8.60	73.877
total	1.000	1194	1194		457.464

test statistic X² =457.464

p value =0.0000

as test statisitc is signfiicantly higher therefore we reject null hypothesis and conclude that proportion of male smoker long cancer death is not the same for the four given tar level categories