o
All we need is for the observations to be independent and
collected with randomization.
o
We don’t even care about the shape of the population
distribution!
In fact, this is a fundamental theorem of statistics and it is called the
Central Limit Theorem (CLT)
.
The CLT is surprising:
o
Not only does the histogram of the sample means get closer and
closer to the Normal model as the sample size grows, but this is
true regardless of the shape of the population distribution.
The CLT works better (and faster) the closer the population model
is to a Normal itself.
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ECON 301 (01)  Introduction to Econometrics I
March, 2012
METU  Department of Economics
Instructor: Dr. Ozan ERUYGUR
email:
[email protected]
Lecture Notes
17
It also works better for larger samples.
o
Particularly, samples of size larger than 30,
n
30
The Central Limit Theorem (CLT)
The mean of a random sample
has a
sampling distribution
whose shape can be approximated by a
Normal
distribution.
The
larger
the
sample,
the
better
the
approximation will be.
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 Spring '10
 öcal
 Econometrics, Normal Distribution, Variance, Probability theory, probability density function, Dr. Ozan Eruygur

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