Question

In a study at West Virginia University Hospital, researchers investigated smoking behavior of cancer patients to create a program to help patients stop smoking. They published the results in Smoking Behaviors Among Cancer Survivors (January 2009 issue of the Journal of Oncology Practice.) In this study, the researchers sent a 22-item survey to 1,000 cancer patients. They collected demographic information (age, sex, ethnicity, zip code, level of education), clinical and smoking history, and information about quitting smoking.

The questionnaire filled out by cancer patients at West Virginia University Hospital also asked patients if they were current smokers. The current smoker rate for female cancer patients was 11.6%. 95 female respondents were included in the analysis. For male cancer patients, the current smoker rate was 10.4%, and 67 male respondents were included in the analysis.

Suppose that these current smoker rates are the true parameters for all cancer patients.

Can we use a normal model for the sampling distribution of differences in proportions?

Answer 1

Sol:

verify 10% condition for both p1 and p2.

both sets of data must meet the normal approximation.

That is n1p1^>=10,

n2(1-p1^)>=10

,n2p2^>1=10,

n2*(1-p2^)>=10

p1^=proportion of female stil smoking=0.116

n1p1^=95*0.116= 11.02>10

n2*(1-p1^)=95*(1-0.116)=83.98>10

10% success and 10% failure condition is verfied for p1^

verify 10% condition for p2^

p2^=proportion of male stil smoking=10.4%=0.104

n2*p2^=67*0.104=6.968<10

but expected success conditions is not satisfied.

n2*(1-p2^)=67*(1-0.104)=60.032>10

expected failure conditions is satisfied.

No,we cannot use a normal model for the sampling distribution of differences in proportions.