Sample size for a target margin of error

Question

You want to estimate the mean daily foot traffic at a store to within a margin of error of $E = 10$ people, with 95% confidence. From past records, the day-to-day standard deviation is about $\sigma = 45$ people.

How many days of data do you need at minimum?

Accepted Answer

Setup. The margin of error of a z interval is E = z^{}\,\sigma/\sqrt{n}. Solve for n: n = \left(\frac{z^{}\sigma}{E}ight)^{2}. For 95% confidence, z^{} = 1.96. Compute. n = \left(\frac{1.96 	imes 45}{10}ight)^{2} = \left(\frac{88.2}{10}ight)^{2} = (8.82)^{2} = 77.79. Sample size must be a whole number, and you always round up to be sure the margin is met, so n = 78. Interpret. Rounding up, not to nearest, matters: 77 days would give a slightly larger margin than 10. Always ceiling the result. Takeaway. To hit a target margin of error, invert the margin formula and round up. The require…

Sample size for a target margin of error

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