In preliminary tests of a vaccine that may help smokers quit by reducing the "rush" from tobacco, 64 subjects who wanted to quit smoking were given either a placebo or the vaccine. Of the 32 in the placebo group, only 3 quit smoking for 30 days (the U.S. Food and Drug Administration's criterion for smoking cessation) compared with 11 of the vaccine group.
(a) Assuming equal sample sizes, find the 95 percent confidence interval for the difference in proportions. What does it suggest?
(b) Why is the sample size a problem here?