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Submitted by gfj100 on Wed, 11/11/2009  12:00
The
central limit theorem
states that if a large enough sample is taken (typically
n
> 30) then
the sampling distribution of
is approximately a normal distribution with a mean of μ and a
standard deviation of
. Since in practice we usually do not know μ or σ we estimate these
by
and
respectively. In this case
s
is the estimate of σ and is the standard deviation of the
sample. The expression
is known as the standard error of the mean, labeled
s.e.(
)
Simulation: Generate 500 samples of size heights of 4 men. Assume the distribution of male
heights is normal with mean
m
= 70" and standard deviation s = 3.0". Then find the mean of each
of 500 samples of size 4.
Here are the first 10 sample means:
70.4 72.0 72.3 69.9 70.5 70.0 70.5 68.1 69.2 71.8
Theory says that the mean of (
) =
μ
=
70
which is also the Population Mean and SE(
)
=
=
=
1.50.
Simulation shows: Average (500
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 Spring '11
 AndyRegards
 Central Limit Theorem, Normal Distribution, Standard Deviation

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