The distribution that is formed by all possible values of a statistic is known as the sampling distribution.
A sampling distribution is a probability distribution of a statistic that is obtained from a large number of samples drawn from a population. It describes the distribution of all possible values of a statistic that could be obtained from the population.
For example, if you were to take multiple samples of size 30 from a population and calculate the mean of each sample, the distribution of those sample means would be the sampling distribution of the mean.
The sampling distribution is an important concept in inferential statistics because it allows us to make inferences about the population based on the sample data. For example, we can use the sampling distribution to construct confidence intervals and perform hypothesis tests.
Here are some key properties of a sampling distribution:
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It is a probability distribution. This means that it describes the likelihood of observing different values of the statistic.
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It is centered around the true population parameter. This means that the mean of the sampling distribution is equal to the population parameter.
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Its shape is determined by the distribution of the population and the sample size.
Understanding the sampling distribution is crucial for understanding the principles behind hypothesis testing and confidence intervals. It allows us to make informed decisions about the population based on the sample data.
