Question

Which of the following describe(s) the standard error of the mean?

• A. It is the standard deviation of the sampling distribution of the mean
• B. It reflects the accuracy with which sample means estimate the population mean
• C. It is the difference between mean and standard deviation of a distribution
• D. It is the standard deviation of a stratified sample

Hint:

Remember: $SE_{\bar X}= \text{SD}/\sqrt{n}$. As $n$ increases, SEM decreases \Rightarrow estimates become more precise.

Answer 1

The Correct Option is A, B

Step 1: Definition. The standard error of the mean (SEM) is the standard deviation of the sampling distribution of the sample mean: $SE_{\bar X}=\dfrac{\sigma}{\sqrt{n}}$ (or $s/\sqrt{n}$ when $\sigma$ is unknown). $\Rightarrow$ (A) is true.

Step 2: Interpretation. A smaller SEM means sample means cluster more tightly around the population mean, i.e., higher precision/accuracy of the estimate. $\Rightarrow$ (B) is true.

Step 3: Eliminate distractors. (C) is a meaningless “difference” and not a definition; (D) confuses SEM with a sample’s own SD. Both are false.
Thus, the correct choices are \fbox{(A) and (B)}.