Sampling Distributions and the Central Limit Theorem
Whenever we select a random sample from a population, collect data from the members of the
sample, and summarize the data values in the form of a statistic, that statistic is a random variable
(depending on which random sample we happen to choose from the population), and thus has an
associated probability distribution, called a
sampling distribution
.
The form of the sampling
distribution will, in general, depend on the type of statistic we are using.
However, there are certain
general properties shared by all sampling distributions.
There is also a rather remarkable fact from
probability theory that says that, under very general conditions and for large sample sizes, all
sampling distributions tend to have approximately the same form.
Random Sampling distribution principles:
•
Even if the underlying distribution isn’t normal, the sampling distribution can be close
enough to normal to be able to use it.
(This is a consequence of the Central Limit
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This note was uploaded on 07/28/2011 for the course STA 2014 taught by Professor Staff during the Fall '10 term at University of Florida.
 Fall '10
 Staff
 Statistics, Central Limit Theorem

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