If you repeatedly take samples from a population and calculate the sample mean, the resulting distribution is called the sampling distribution of the mean. This statement is:

If you repeatedly take samples from a population and calculate the sample mean, the resulting distribution is called the sampling distribution of the mean. This statement is:

• A. True
• B. False
• C. The distribution of population values.
• D. The distribution of the sampling errors.

Answer: (A)

The concept being tested is the sampling distribution of the mean. When you repeatedly take samples from a population and compute the mean of each sample, the collection of those sample means forms a distribution called the sampling distribution of the mean. This distribution reflects how the sample mean would vary across different samples and is centered at the population mean μ, with spread given by the standard error (σ/√n, or s/√n in practice). The shape becomes approximately normal as sample size grows, thanks to the Central Limit Theorem, even if the population itself isn’t normally distributed. It’s not the distribution of population values—that would describe the population distribution—or the distribution of sampling errors, which concerns the differences between sample means and the true population mean. So the statement is true.

The concept being tested is the sampling distribution of the mean. When you repeatedly take samples from a population and compute the mean of each sample, the collection of those sample means forms a distribution called the sampling distribution of the mean. This distribution reflects how the sample mean would vary across different samples and is centered at the population mean μ, with spread given by the standard error (σ/√n, or s/√n in practice). The shape becomes approximately normal as sample size grows, thanks to the Central Limit Theorem, even if the population itself isn’t normally distributed. It’s not the distribution of population values—that would describe the population distribution—or the distribution of sampling errors, which concerns the differences between sample means and the true population mean. So the statement is true.