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.