From: Stan Hilliard
Date: 10/14/2005
Time: 9:46:52 PM
Here is a formula for n=sample size that will give you a margin of error that you choose. It is accurate when the sample is no more than 1/10th of the population: 3000/10=300. That rule of thumb can be violated moderately without too much effect.
n = sample size
n = Z*Z*(p*(1-p))/(d*d)
(I don't know how to indicate "squared" with this editor.)
d = margin of error. (+ or - d) If the sample result is p=0.5 fraction (50%) favorable, then the confidence interval is 0.5 +-d. For example 0.50 +- 0.10. So the interval estimate of the population fraction favorable is 0.40 to 0.60. The smaller the margin of error, the larger the sample size has to be.
Z = normal deviate. For 2-sided 90% confidence limits, Z=1.65, For 95% confidence Z=1.96. The larger Z is, the larger the sample.
p = fraction of responses favorable (or unfavorable). You have to guess at this until you get the data, but a safe pick is 0.5 (50%), as that gives the largest n.
Example: For a margin of error d=0.10, and 95% confidence,
n = 1.96*1.96*(0.5*(1-0.5))/(0.1*0.1) = 96 kids
You could try different margins of error (d) to see how the sample size will change. Then use your judgement to pick a practical trade-off between sample size and margin of error.