According to this page:
http://mathworld.wolfram.com/StandardError.html
It says: "It therefore estimates the standard deviation of the sample mean based on the population mean."
So for example, if I have an entire population of 5 people, their age is {8,6,7,1,5}, then its stddev is about 2.702 and mean is 5.4
If I take random sample of size 3, maybe I will come up with {8,1,5}, then its stddev is about 3.512, mean is 4.667
As I increase the size of the sample and finally come to 5, that is, the sample is exactly equal to the entire poplution in this example. Then the standard error of the mean between [the sample] and [the entire population] should theoretically be zero.
But when I use this formula SE = σ/sqrt(n),
Since I already know the stddev of the entire population, which is 2.702 and I also know the size of the sample is now 5.
Substituting these values into the formula:
SE=2.702/sqrt(5)=1.208
The SE is not equal to zero. Why?
Thanks a lot.
2007-11-16
14:09:21
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