Ahlers, Zachary2017-07-062017-07-062017-08-01http://hdl.handle.net/2097/35762Among the most used statistical concepts and techniques, seen even in the most cursory of introductory courses, are the confidence interval, binomial distribution, and sample size estimation. This paper investigates a particular case of generating a confidence interval from a binomial experiment in the case where zero successes are expected. Several current methods of generating a binomial proportion confidence interval are examined by means of large-scale simulations and compared in order to determine an ad-hoc method for generating a confidence interval with coverage as close as possible to nominal while minimizing width. This is then used to construct a formula which allows for the estimation of a sample size necessary to obtain a sufficiently narrow confidence interval (with some predetermined probability of success) using the ad-hoc method given a prior estimate of the probability of success for a single trial. With this formula, binomial experiments could potentially be planned more efficiently, allowing researchers to plan only for the amount of precision they deem necessary, rather than trying to work with methods of producing confidence intervals that result in inefficient or, at worst, meaningless bounds.en-US© the author. This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).http://rightsstatements.org/vocab/InC/1.0/Binomial proportionZero successesSample size estimationRule of threeReport