Exact Computation of Minimum Sample Size for Estimating Proportion of Finite Population

In this paper, we develop an exact method for the determination of the minimum sample size for estimating the proportion of a finite population with prescribed margin of error and confidence level. By characterizing the behavior of the coverage probability with respect to the proportion, we show that the computational complexity can be significantly reduced and bounded regardless population size.

💡 Research Summary

The paper addresses a fundamental problem in finite‑population statistics: determining the smallest sample size required to estimate a population proportion with a pre‑specified margin of error (ε) and confidence level (1‑α). While classical textbooks often rely on normal approximations or conservative inequalities (e.g., Chebyshev, Hoeffding) that become overly cautious when the population is finite or the true proportion is near the boundaries (0 or 1), this work proposes an exact, computationally tractable method based on the hypergeometric distribution, which is the exact sampling distribution for draws without replacement from a finite population.

The authors begin by defining the coverage probability C(p; n, ε) as the probability that the confidence interval (