The Gallop poll explains sampling error in the following way:
Statisticians over the years have developed quite specific ways of measuring the accuracy of samples -- so long as the fundamental principle of equal probability of selection is adhered to when the sample is drawn.
For example, with a sample size of 1,000 national adults, (derived using careful random selection procedures), the results are highly likely to be accurate within a margin of error of plus or minus three percentage points. Thus, if we find in a given poll that President Clinton's approval rating is 50%, the margin of error indicates that the true rating is very likely to be between 53% and 47%. It is very unlikely to be higher or lower than that.
To be more specific, the laws of probability say that if we were to conduct the same survey 100 times, asking people in each survey to rate the job Bill Clinton is doing as president, in 95 out of those 100 polls, we would find his rating to be between 47% and 53%. In only five of those surveys would we expect his rating to be higher or lower than that due to chance error.
1. Do you agree with this explanation? Can you suggest any wording changes that might improve it?