Sample size for a confidence interval
Section of Confidence intervals, part of Statistical inference
Sample size for a confidence interval
| Type | Section |
| Taught in | Confidence intervals |
| Part | Statistical inference |
For a normal mean with known \sigma, the half-width of the interval is E=z_{1-\alpha/2}\,\sigma/\sqrt n. Solving for n, a half-width of at most E needs
n\ge\Bigl(\frac{z_{1-\alpha/2}\,\sigma}{E}\Bigr)^2.
Halving the half-width needs four times the sample. For a proportion the same calculation with \sigma^2=p(1-p)\le1/4 gives the conservative n\ge z_{1-\alpha/2}^2/(4E^2). A poll accurate to \pm3 percentage points with 95% confidence needs about 1.96^2/(4\times0.03^2)\approx1068 people, whatever the size of the population.
A confidence interval is a pivot solved for the parameter. The coverage probability is computed before the data are seen, over all the samples that might have been drawn. The numerical interval reported afterwards is not assigned that probability.
Used in
See also
Confidence interval · Pivot · One-sample t pivot · Pooled variance · Two-sample t pivot · Variance-ratio F pivot · Wald interval · Coverage