A sampling distribution is the probability distribution of a given statistic based on a random sample. It reflects how the statistic would vary if you repeatedly sampled from the same population.
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The mean of the sampling distribution of the sample mean is equal to the population mean ($\mu$).
The standard deviation of the sampling distribution, known as the standard error, decreases as sample size increases.
According to the Central Limit Theorem, for sufficiently large sample sizes, the sampling distribution of the sample mean will be approximately normally distributed regardless of the population's distribution.
The shape of a sampling distribution depends on both the size of the sample and the shape of the population distribution.
Sampling distributions are fundamental for constructing confidence intervals and conducting hypothesis tests.
Review Questions
What is the relationship between the population mean and the mean of its sampling distribution?
How does increasing sample size affect the standard error in a sampling distribution?
Explain why sampling distributions are important in inferential statistics.
States that, for a sufficiently large sample size, the sampling distribution of the sample mean will be approximately normally distributed regardless of population shape.