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O all we need is for the observations to be

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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 e-mail: [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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