Re: Ask for help on sample size decision for a non-normal distribution
- From: "m00es" <m00es@xxxxxxxxx>
- Date: 30 Dec 2006 10:03:19 -0800
Jane wrote:
Hello, group.
I have a problem on sample size decision. supposed that for a
sysmmetric distribution with mean=0 (but it is non-normal). How can I
decide the sample size that can garuntee that guarantee that the mean
of sample =0 with certian power.
Easy. The answer is: infinity.
Let m be the sample mean calculated from n observations taken from a
continuous distribution with expected value mu = 0. The probability
that m is exactly 0 for finite n is zero.
However, under the assumption of normality, we know that the interval
m +- 1.96 sqrt( sigma^2 / n )
will include the value mu with probability .95, where sigma^2 is the
variance in the population. Unless you are dealing with some nasty
distribution, we know, based on the central limit theorem, that this
interval will also capture mu with approximately .95 probability as
long as n is not too small. So, if you know sigma^2, you can solve for
n to figure out how large n has to be in order for the interval to be
of a certain desired size.
m00es
.
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