For example, if 50 percent of a sample of 1,000 randomly selected Americans said they favor recycling laws, in 95 cases out of 100, 50 percent of the entire population in the U.S. would also have given the same response had they been asked, give or take 3 percentage points (i.e., the true proportion could be 47 percent or 53 percent).
The bigger the sample, the smaller the margin of error, but once you get past a certain point -- say, a sample size of 800 or 1,000 — the improvement is very small.
