Sample size to hit a target standard error

Question

You want the standard error of your estimated mean to be at most 0.25. The population standard deviation is \sigma = 3. How many observations do you need?

Accepted Answer

This version skips confidence levels and z-scores entirely: you have a target for the standard error itself. Recall the standard error of the mean: 	ext{SE} = \frac{\sigma}{\sqrt{n}}. Set it equal to the target and solve for n. Rearranging gives n = \left(\frac{\sigma}{	ext{SE}}ight)^2 = \left(\frac{3}{0.25}ight)^2 = (12)^2 = 144. So 144 observations bring the standard error down to exactly 0.25. (If the target had come out fractional, you would round up.) Takeaway. To hit a target standard error, use n = (\sigma/	ext{SE})^2: it is the same \sqrt{n} law seen from the other side, cuttin…

Sample size to hit a target standard error

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