Exact Computation of Minimum Sample Size for Estimation of Binomial Parameters

Understand

It is a common contention that it is an ``impossible mission'' to exactly determine the minimum sample size for the estimation of a binomial parameter with prescribed margin of error and confidence level.

• In this paper, we investigate such a very old but also extremely important problem and demonstrate that the difficulty for obtaining the exact solution is not insurmountable.
• Unlike the classical approximate sample size method based on the central limit theorem, we develop a new approach for computing the minimum sample size that does not require any approximation.
• Moreover, our approach overcomes the conservatism of existing rigorous sample size methods derived from Bernoulli's theorem or Chernoff bounds.