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Abstract In this article, we point out some interesting relations between the exact test and the score test for a binomial proportion p. Based on the properties of the tests, we propose some approximate as well as exact methods of computing sample sizes required for the tests to attain a specified power. Sample sizes required for the tests are tabulated for various values of p to attain a power of 0.80 at level 0.05. We also propose approximate and exact methods of computing sample sizes needed to construct confidence intervals with a given precision. Using the proposed exact methods, sample sizes required to construct 95% confidence intervals with various precisions are tabulated for p = .05(.05).5. The approximate methods for computing sample sizes for score confidence intervals are very satisfactory and the results coincide with those of the exact methods for many cases. Keywords: Clopper–Pearson intervalCoverage probabilityExpected lengthOne-sided limitsSizesWilson intervalMathematics Subject Classification: Primary 62H15Secondary 62H17 Notes ∗The approximate sample size in (18) is the reported exact sample size for the score interval minus the number in the superscript.
Krishnamoorthy et al. (Mon,) studied this question.