Sampling distribution

Definition

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.

5 Must Know Facts For Your Next Test

1. The mean of the sampling distribution of the sample mean is equal to the population mean ($\mu$).
2. The standard deviation of the sampling distribution, known as the standard error, decreases as sample size increases.
3. 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.
4. The shape of a sampling distribution depends on both the size of the sample and the shape of the population distribution.
5. 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.

Related terms

Central Limit Theorem:

States that, for a sufficiently large sample size, the sampling distribution of the sample mean will be approximately normally distributed regardless of population shape.

Standard Error:

The standard deviation of a sampling distribution. It measures how much a statistic differs from one random sample to another.

Confidence Interval:

A range of values derived from a sample statistic that is likely to contain the value of an unknown population parameter.