Define the term 'sampling distribution' of a statistic.

Define the term 'sampling distribution' of a statistic.

• A. The probability distribution of that statistic over repeated samples from the population.
• B. The distribution of the population parameter.
• C. The distribution of sample means only.
• D. The distribution of residuals.

Answer: (A)

A sampling distribution is the probability distribution you get for a statistic when you repeat the sampling process many times and compute that statistic each time. It shows how the statistic would vary due to random sampling alone. For example, the sampling distribution of the sample mean describes all the possible values the average of samples could take across repeated samples, and its center and spread relate to the population mean and the standard error. This concept applies to any statistic, not just the mean. It’s not the distribution of the population parameter (the parameter is fixed, not random), and it isn’t about residuals (which come from a model’s errors, not from drawing samples).

A sampling distribution is the probability distribution you get for a statistic when you repeat the sampling process many times and compute that statistic each time. It shows how the statistic would vary due to random sampling alone. For example, the sampling distribution of the sample mean describes all the possible values the average of samples could take across repeated samples, and its center and spread relate to the population mean and the standard error.

This concept applies to any statistic, not just the mean. It’s not the distribution of the population parameter (the parameter is fixed, not random), and it isn’t about residuals (which come from a model’s errors, not from drawing samples).