What Sampling distribution is
Sampling distribution is the probability distribution of a statistic obtained by taking repeated samples of the same size from a given population. It describes how the sample statistic is likely to vary from sample to sample.
Steps for Sampling distribution:
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Select a population of interest.
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Define the sample statistic of interest.
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Select a sample size.
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Take repeated samples of the same size from the population of interest.
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Calculate the sample statistic for each sample.
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Plot the sample statistics in a histogram or a frequency distribution. This is the sampling distribution.
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Examine the sampling distribution to make inferences about the population parameters.
Examples
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Estimating a population mean: Sampling distributions can be used to estimate population means by taking a random sample of a population and calculating the mean of the sample.
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Estimating a population proportion: Sampling distributions can be used to estimate population proportions by taking a random sample of a population and calculating the proportion of individuals in the sample with a particular characteristic.
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Testing a hypothesis: Sampling distributions can be used to test a hypothesis by taking a random sample of a population and using the sample data to test the hypothesis.