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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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 Ray Koopman Posts: 3,383 Registered: 12/7/04
Re: Sampling From Finite Population with Replacement
Posted: Sep 29, 2010 2:54 PM

On Sep 28, 8:54 pm, Cagdas Ozgenc <cagdas.ozg...@gmail.com> wrote:
> On 29 Eylül, 02:23, Ray Koopman <koop...@sfu.ca> wrote:
>> On Sep 28, 11:48 am, Cagdas Ozgenc <cagdas.ozg...@gmail.com> wrote:
>>> [...]
>>> Now we are looking at a sample of a sample. This means that no matter
>>> what you do, you will never find the mean of the normal distribution
>>> (Mu) by repeated sampling. It doesn't matter whether you do it with
>>> replacement or without replacement.
>>>
>>> You will end up calculating the mean of the population, which will
>>> be slightly or significantly different from Mu depending on how many
>>> students entered UC Davis in year 2005. This means that our samples
>>> of 100 students will be an unbiased estimate of the population mean
>>> but a biased estimate of Mu.

>>
>> The population mean is an unbiased estimate of the generator mean.
>> The sample mean is an unbiased estimate of the population mean,
>> and therefore of the generator mean.

>
> I think you have a point here. But as you can see that there is a
> problem with consistency.
>
> Let's say that generator mean is Mu, and population mean is Mu + Eps.
> And I take as you suggest Eps is a random error not a systematic error
> (not a bias).
>
> Now as you take more and more sample means, you will see that they
> will start to gather around Mu+Eps not Mu. Now do we have a random
> error or a systematic error?

It all depends on whether we're talking about the conditional
distribution of the sample mean, given the population mean; or the
unconditional (or marginal) distribution of the sample mean. As an
estimate of the generator mean, the ssmple mean is conditionally
biased but marginally unbiased.