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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
Re: Sampling From Finite Population with Replacement
Posted: Sep 28, 2010 11:54 PM

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?