Sampling Distribution

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Sampling Distribution
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• In a statistical application, we take a random
  sample from our population. We make measurements
  on the items in the sample and compute a
  statistic say .
• The value of the statistic depends on which items
  are selected for the sample. is a random
  variable. Different samples yield different
  values of .

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What is a sampling distribution?

• The sampling distribution of a statistic is the
  distribution of values taken by the statistic in
  all possible samples of the same size from the
  same population.

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Statistics Estimate Parameters

• For example
• The sampling distribution of a statistic lets us
  understand how good it can be expected to be in
  estimating a parameter.
• We want the sampling distribution to be centered
  at the value of the parameter and to have little
  variation.
• The standard error of an estimator is the
  standard deviation of its sampling distribution.