Question

20. The results of a recent study regarding smoking and three types of illness are shown in the following table.

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Illness	Non-Smokers	Smokers	Totals
Emphysema	50	150	200
Heart problem	50	150	200
Cancer	100	500	600
Totals	200	800	1000

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We are interested in determining whether or not illness is independent of smoking.

a.	State the null and alternative hypotheses to be tested.
b.	Show the table of the expected frequencies and determine the test statistic.
c.	The null hypothesis is to be tested at the .01 level. Determine the critical value for this test.
d.	What do you conclude?

Answer 1

Ans:

a)

H₀: illness is independent of smoking.

H_a: illness is not independent of smoking.

b)

	Observed(fo)
Illness	Non-Smokers	Smokers	Totals
Emphysema	50	150	200
Heart problem	50	150	200
Cancer	100	500	600
Totals	200	800	1000
	Expected(fe)
Illness	Non-Smokers	Smokers	Totals
Emphysema	40	160	200
Heart problem	40	160	200
Cancer	120	480	600
Totals	200	800	1000
	Chi square=(fo-fe)^2/fe
Illness	Non-Smokers	Smokers	Totals
Emphysema	2.500	0.625	3.125
Heart problem	2.500	0.625	3.125
Cancer	3.333	0.833	4.167
Totals	8.333	2.083	10.417

Test statistic:

Chi square=10.417

df=(3-1)*(2-1)=2

p-value=CHIDIST(10.417,2)=0.0055

c)

Critical chi square=CHIINV(0.01,2)=9.21

d)As,test statistic is greater than critical value,we reject the null hypothesis.

There is sufficient evidence to conclude that illness is not independent of smoking.