Which statement correctly defines the standard error?

Which statement correctly defines the standard error?

• A. The standard deviation of the sampling distribution of the mean
• B. A measure of population variability
• C. The mean of the sampling distribution
• D. The standard error of the population variance

Answer: (A)

How much a sample mean would vary if you repeated the study many times is captured by the standard error. The standard error is the standard deviation of the sampling distribution of the mean, meaning it measures how spread out the sample means are around the true population mean. It reflects precision: a smaller standard error means the sample mean is a more accurate estimate of the population mean. If the population standard deviation is known, the standard error is that value divided by the square root of the sample size; with an estimate from the data, you use the sample standard deviation divided by the square root of n. This concept describes dispersion of the sampling distribution, not variability within the population itself. Population variability is described by the population standard deviation, and the mean of the sampling distribution equals the population mean, not its dispersion.

How much a sample mean would vary if you repeated the study many times is captured by the standard error. The standard error is the standard deviation of the sampling distribution of the mean, meaning it measures how spread out the sample means are around the true population mean. It reflects precision: a smaller standard error means the sample mean is a more accurate estimate of the population mean. If the population standard deviation is known, the standard error is that value divided by the square root of the sample size; with an estimate from the data, you use the sample standard deviation divided by the square root of n. This concept describes dispersion of the sampling distribution, not variability within the population itself. Population variability is described by the population standard deviation, and the mean of the sampling distribution equals the population mean, not its dispersion.