Question

Suppose that you are interested in determining whether the advice given by a physician during a routine physical examination is effective in encouraging patients to stop smoking. In a study of current smokers, one group of patients was given a brief talk about the hazards of smoking and was encouraged to quit. A second group received no advice pertaining to smoking. All patients were given a follow-up exam. In the sample of 114 patients who had received the advice, 11 reported that they had quit smoking; in the sample of 96 patients who had not, 7 had quit smoking.

(a) Estimate the true difference in population proportions p1 - p2.

(b) Construct a 95% confidence interval for this difference.

(c) At the 0.05 level of significance, test the null hypothesis that the proportions of patients who quit smoking are identical for those who received advice and those who did not.

(d) Do you believe that the advice given by physicians is effective? Why or why not?

Answer 1

Solution-A:

Estimate the true difference in population proportions p1 - p2

=11/114-7/96

= 0.09649123-0.07291667

=0.02357456

Solution-B:

pbar=x1+x2/n1+n2

=(11+7)/(114+96)

= 0.08571429

z crit for 95%=1.96

95% confidence interval for difference in proportions is

(p1^-p2^)+_zcrit*sqrt(p1^*(1-p1^)/n1+p2^*(1-p2^)/n2)

(0.09649123-0.07291667)+--1.96*sqrt((0.09649123*(1-0.09649123)/114)+(0.07291667*(1-0.07291667)/96))

0.02357456+- 0.07511961

-0.05154505, 0.09869417

-0.05154505<p1-p2< 0.09869417

95% lower limit for p1-p2=-0.05154505

95% upper limit for p1-p2=0.09869417

Solution-c:

Ho:p1=p2

Ha:p1 not =p2

alpha=0.05

z=p1^-p2^/sqrt(pbar*(1-pbar)*(1/n1+1/n2))

pbar=x1+x2/n1+n2

=(11+7)/(114+96)

= 0.08571429

z=(0.09649123-0.07291667)/sqrt(0.09649123*(1-0.09649123)/114+0.07291667*(1-0.07291667)/96))

z= 0.6079312

z crit for 95%=+-1.96

z statistic>z critical

Fail to reject Ho

Conclusion:

there is sufficient statistical evidence at 5% level of signifcance to conclude that

proportions of patients who quit smoking are identical for those who received advice and those who did not.

Solution-d:

advice given by physicians is not effective

as there is sufficient statistical evidence at 5% level of significance to conclude that

proportions of patients who quit smoking are identical for those who received advice and those who did not.