Hi
Given a population of 300 and assuming a population S.D of around 2
(coincides with 2 S.D from the mean) I make it around 75 responses to
achieve a standard error of 0.2.
The central limit theorem adjusted for the finite population case yields a
Normal(mu, (1-n/N)*sigma^2/n), where n is the number of responses and N is
the population size. The approximation usually works well for large n. Now
putting all this together we know that the standard error here is
sqrt(sigma^2*(1-n/N)/n).
Thus, solving the above equation to yield 0.2, when sigma=2 and N=300, we
obtain n=75 roughly.
So we need around 75 responses out of 300, which is a response rate of
around 25% which is achievable.
Note: this all depends on the choice of sigma above, but 2 seems like a
fair estimate of the population S.D. However, if it was smaller you need a
lower number of responses and vice versa to achieve a 0.2 standard error.
Hope that helps.
Siva
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