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    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...

    Q:

    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 isnít an equation to figure this out is there?

    Thanks so much in advance!

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    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.

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