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?