# Z-test for One Population Proportion

I am completing a series of questions for this problem and I think I am following but one throws me off.

The problem is a common one:

In a study of smokers who tried to quit smoking with nicotine patch therapy 39 were smoking one year after the treatment and 32 were not smoking one year after the treatment. We want to use a 0.05 significance level to test the calim that among smokers who try to quit with nicotine patch therapy the majority are smoking a year after the treatment.

From this I derived: H0:p=0.5 and Ha:p>0.5

 P0=0.5, n=71, x=39, a=0.05

Sample proportion = 39/71 or 0.5493

Crtical value for a right tale test Zc=1.64
z = 0.5493-0.5 / Sqrt 0.5(1-0.5)/71
z statistic =0.831
z is < Zc so Ho is not rejected

p=0.2031 which is > a 0.05 so once again H0 is not rejected
The 95% CI for p is 0.434 < p <0.665


There are questions for the null hypothesis, alternative hypothesis, the critical value, the p value, the standard score, describe a type I and II error and a conclusion.. All of which I believe I have..

The question that throws me off is:

What is the p value if the claim is modified to state the proportion IS equal to 0.5?

If you can help shed some light on this one portion of this problem I would appreciate it.. Thank you.

• The hypothesis is not clear. The
– user10619
Commented Jul 16, 2017 at 13:23
• Working on several ideas with no specific hypotheses. Be sure what are your objectives ? Do you want to check effect of treatment or tendency to resume ? Avoid issues that concern testing. Edit your question.
– user10619
Commented Jul 16, 2017 at 13:39