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Topic: Sampling From Finite Population with Replacement
Replies: 28   Last Post: Sep 30, 2010 6:30 AM

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 cagdas.ozgenc@gmail.com Posts: 58 Registered: 3/29/06
Sampling From Finite Population with Replacement
Posted: Sep 24, 2010 6:20 AM

In statistics text books it is proposed that sampling from a finite
population with replacement is equivalent to sampling from an infinite
population. I find this somewhat misleading.

Suppose that we have a population of size N generated by random
variable Normal(MeanM, StdDevM). Then take samples of size n < N from
this population and calculate average (let's call it MeanS).

MeanS = (1/n)*sum of samples

There is no way you can estimate MeanM in an unbiased fashion. You can
only estimate population mean (let's call it MeanP) which is not
equal to MeanM, the mean of random variable that generated the
population.

Is my thinking flawed? Or do we always infer about an hypothetical
infinite population?