Discussion
If the standard deviation of a population is 20 and the standard error of mean is 4, then the sample size is
Answer: A
The sample size is 25, option A. The standard error of the mean is the population standard deviation divided by the square root of the sample size.
\[ \begin{aligned} SE &= \frac{\sigma}{\sqrt{n}} \\ 4 &= \frac{20}{\sqrt{n}} \\ \sqrt{n} &= 5 \\ n &= 25 \end{aligned} \]
Option C, 5, is the value of the square root and is what you get if you stop one step early. Option B, 80, comes from multiplying 20 by 4, and option D, 100, from taking n = 5 squared times 4. A quick check: 20 divided by the square root of 25 is 20 divided by 5, which is 4.
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