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Why does standard error not involve population size?

When calculating confidence intervals for population parameters, the population size is never a factor, rather sample size and the estimated parameter are used.

It seems to me very counter-intuitive that to assert with a certain confidence that a certain view has certain probability, one requires the same sample size regardless of whether the population is 2K persons or 2M persons.

Why is the confidence of estimated parameters of normal distributions independent of the population size?

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jsj
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  • The standard calculations that I suspect you are thinking of assume that the population is infinite. If the population is finite, and not very large, the appropriate calculations can be more complicated. (If the population is finite, but very large relative to the sample size, I believe the standard calculations are still approximately right.) – gung - Reinstate Monica Oct 17 '12 at 15:19
  • Also closely related: http://stats.stackexchange.com/questions/166, http://stats.stackexchange.com/questions/5158 – whuber Oct 17 '12 at 16:14

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