Margin of Error/Sample Size...

I have another questions that I am not totally sure of the answer....
It has to do with the size of a sample. This is the question...


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 les than +/- 3 percentage points, equal to +/- 3 percentage points, or greater than +/- 3 percentage points? Explain your answer.

My take on this is that if you increase the sample size, your margin of error decreases. But I am wondering if it might stay somewhat equal to +/- 3 percentage points because the difference between 1060 and 1500 isn't really that huge? Am I right to say that the margin of error will be less than +/- 3 percentage points? There isn’t an equation to figure this out is there?

Thanks so much in advance!


TS Contributor
You would be correct - in general, as sample size increases, margin of error decreases.

For proportions, the formula is:

n = (p*q/d^2) * z^2

p = proportion
q = 1-p
d = margin of error
z = z-score for the level of confidence

For your example, it would decrease to somewhere around +/- 2.5 or 2.6, so not much of a difference.