Consider the situation: A Gallup Poll in 2001 asked 1060 randomly selected adults, “How would you rate the overall quality of the environment in this country today-as excellent, good, only fair, or poor?” In all, 46% of the sample rated the environment as good or excellent. Gallup said that “one can say with 95% confidence that the margin of sampling error is ± 3 percentage points.”
If the poll had interviewed 1500 persons rather than 1060, (and still found 46% rating the environment as good or excellent), would the margin of error for 95% confidence be less than ± 3 percentage points, equal to ± 3 percentage points, or greater than ± 3 percentage points? Explain your answer.
Answer: The margin error for 95% confidence would be less than ± 3 percentage points, because the margin of error decreases with the sample size. In fact, the MOE is computed as
which clearly shows that if n increases, the MOE decreases.