Abstract
Approximate confidence limits for the probability of success in a trial are derived under the assumption that the sample is large and the successive trials are governed by a stationary first-order Markov chain model. The conditional probability of a success, given a success, is a nuisance parameter and is replaced by a sample estimate. Five different approximations are given: normal distribution, Edgeworth series two-term and four-term, Pearson system, and modified Poisson-Anderson-Burstein. Results of Gabriel (1959) and Klotz (1973) are used. Methods for designing the experiment so as to achieve a specified precision are given
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