Sample size for a one mmHg margin

Question

A clinician wants to estimate mean systolic blood pressure to within a margin of error of $E = 1$ mmHg, with 95% confidence. The population standard deviation is $\sigma = 8$ mmHg.

What is the minimum sample size, and what happens to it if the target margin is halved?

Accepted Answer

Setup. Use n = (z^{}\sigma/E)^{2} with z^{} = 1.96. Compute. n = \left(\frac{1.96 	imes 8}{1}ight)^{2} = (15.68)^{2} = 245.86. Round up: n = 246. Halving the margin. Because n \propto 1/E^{2}, replacing E = 1 with E = 0.5 multiplies the required size by 4, to about 983. Twice the precision, four times the data. Takeaway. A one-unit margin against an 8-unit spread already needs hundreds of observations, and the 1/E^{2} law means each further squeeze in the margin is dramatically more expensive.

Sample size for a one mmHg margin

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