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.