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Sample Size Calculation — Given Margin of Error

For means: n ≥ (z*σ/ME)². For proportions: n ≥ z*²·p*(1−p*)/ME² (use p*=0.5 if p unknown).

StatisticsCommon Core UNC-4.CINFVerified correct ✓

Worked examples

A researcher wants to estimate a population mean with a 95% confidence interval and a margin of error no more than 4. The population standard deviation is σ = 10. (Use z* = 1.96.) What is the minimum sample size needed?
Answer: 25
A researcher wants to estimate a population mean with a 95% confidence interval and a margin of error no more than 5. The population standard deviation is σ = 25. (Use z* = 1.96.) What is the minimum sample size needed?
Answer: 97

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Confidence Interval for a Population Mean (t-interval)Confidence Interval for a Population Proportion (z-interval)

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