Which distribution represents the theoretical distribution of a sample statistic across all possible samples?

Which distribution represents the theoretical distribution of a sample statistic across all possible samples?

• A. Sampling distribution of the mean
• B. Population distribution
• C. Empirical distribution of the sample
• D. Theoretical sampling distribution of the mean

Answer: (D)

Think of what happens if you could take every possible sample of a given size from a population and compute the statistic (for example, the mean) for each sample. The collection of those computed values forms a distribution—the sampling distribution. When we say the theoretical sampling distribution of the mean, we’re talking about the distribution that theory describes for the mean across all possible samples, not just what you happen to observe in one sample. It has a center at the population mean and a spread called the standard error (the population standard deviation divided by the square root of the sample size). This distinction is what sets it apart from the population distribution (which describes how the variable itself is distributed in the whole population) and from the empirical distribution of the sample (which reflects only the data you collected in one actual sample).

Think of what happens if you could take every possible sample of a given size from a population and compute the statistic (for example, the mean) for each sample. The collection of those computed values forms a distribution—the sampling distribution. When we say the theoretical sampling distribution of the mean, we’re talking about the distribution that theory describes for the mean across all possible samples, not just what you happen to observe in one sample. It has a center at the population mean and a spread called the standard error (the population standard deviation divided by the square root of the sample size). This distinction is what sets it apart from the population distribution (which describes how the variable itself is distributed in the whole population) and from the empirical distribution of the sample (which reflects only the data you collected in one actual sample).