Minimum Sample Size
Determine the minimum sample size needed for a nonparametric tolerance interval to cover at least p of the population with confidence γ, using Wilks' theorem.
Two-sided [X(1), X(n)]:
P(coverage ≥ p) = 1 − n·pn−1 + (n−1)·pn ≥ γ
Find smallest n satisfying the inequality.
P(coverage ≥ p) = 1 − n·pn−1 + (n−1)·pn ≥ γ
Find smallest n satisfying the inequality.
e.g. 0.95 = cover at least 95% of population
e.g. 0.95 = 95% confidence
Minimum Sample Size
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Quick Reference — Minimum n
| Coverage (p) | γ = 0.90 | γ = 0.95 | γ = 0.99 |
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Compute Tolerance Interval
Enter sample data and a confidence level. For each coverage percentage, the table shows the tightest interval bounds (order statistics) that achieve at least γ confidence.
Highlight this row in the results table
Coverage Table