The standard error is defined as the standard deviation of the sampling distribution of the sample mean.

The standard error is defined as the standard deviation of the sampling distribution of the sample mean.

• A. Population standard deviation
• B. Standard error
• C. Margin of error
• D. Confidence coefficient

Answer: (B)

The concept being tested is what the standard error measures: how much the sample mean is expected to vary across repeated samples from the same population. By definition, the standard error is the standard deviation of the sampling distribution of the sample mean. If the population has standard deviation sigma and you draw samples of size n, the spread of those sample means is sigma divided by the square root of n. When sigma isn’t known, we estimate it with the sample standard deviation s, giving se ≈ s / sqrt(n). This shows why larger samples yield more precise estimates of the population mean. The other terms refer to related but different ideas: the population standard deviation describes the spread of individual data points in the entire population; the margin of error is half the width of a confidence interval and depends on the standard error but is not the standard deviation of the sampling distribution itself; the confidence coefficient (confidence level) is the probability that the interval contains the true parameter.

The concept being tested is what the standard error measures: how much the sample mean is expected to vary across repeated samples from the same population. By definition, the standard error is the standard deviation of the sampling distribution of the sample mean. If the population has standard deviation sigma and you draw samples of size n, the spread of those sample means is sigma divided by the square root of n. When sigma isn’t known, we estimate it with the sample standard deviation s, giving se ≈ s / sqrt(n). This shows why larger samples yield more precise estimates of the population mean.

The other terms refer to related but different ideas: the population standard deviation describes the spread of individual data points in the entire population; the margin of error is half the width of a confidence interval and depends on the standard error but is not the standard deviation of the sampling distribution itself; the confidence coefficient (confidence level) is the probability that the interval contains the true parameter.