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Sample Size Requirements for the Back-of-the-Envelope Binomial Confidence Interval
Authors:Myra L. Samuels  Tai-Fang C. Lu
Affiliation:1. Departments of Statistics and Veterinary Pathobiology , Purdue University , West Lafayette , IN , 47907-1399 , USA;2. Provience University , Shalu, Republic of China, Taiwan
Abstract:The simplest approximate confidence interval for the binomial parameter p, based on x successes in n trials, is

 /></span> </p> where <i>c</i> is a suitable percentile of the normal distribution. Because <i>I</i> <sub>0</sub> is so useful in introductory teaching and for back-of-the-envelope calculation, it is desirable to have guidelines for deciding when it provides a good answer. (It is clearly unwise to use <i>I</i> <sub>0</sub> when <i>x</i> is too near 0 or <i>n.</i>) This article proposes such guidelines, based on the criterion that <i>I</i> <sub>0</sub> should differ from the exact Clopper-Pearson confidence interval by an amount that is small compared to the length of the interval.</td>
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Keywords:Binomial distribution  Normal approximation
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