CENTRAL LIMIT THEOREM: STATEMENT
Consider a large population:
Population mean=
Y
μ
Population variance =
Y
2
σ
Take all possible samples of size n from this population and compute the sample means
Y
. The Central Limit Theorem states the following:
1.
The mean of the sampling distribution of the mean is equal to the population
mean (i.e.
Y
Y
E
=
)
(
2.
The variance of the sampling distribution of the mean is equal to the population
variance divided by the sample size (n) i.e.
n
Y
Y
/
2
2
=
(Therefore the
standard deviation (or standard error) of the mean is the population standard
deviation divided by the square root of the number of observations i.e.

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