Quit Smoking:Previous studies suggest that use of nicotine-replacement therapies and antidepressants can help people stop smoking. The New England Journal of Medicine published the results of a double-blind, placebo-controlled experiment to study the effect of nicotine patches and the antidepressant bupropion on quitting smoking. The target for quitting smoking was the 8th day of the experiment.

In this experiment researchers randomly assigned smokers to treatments. Of the 175 smokers taking a placebo, 21 stopped smoking by the 8th day. Of the 288 smokers taking only the antidepressant buproprion, 79 stopped smoking by the 8th day. Calculate the estimated standard error for the sampling distribution of differences in sample proportions.

The estimated standard error---