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Abstract
The binomial model is widely used in statistical applications. Usually, the success probability, p, and its associated confidence interval are estimated from a random sample. Thus, the observations are independent and identically distributed. Motivated by a legal case where some grand jurors could serve a second year, this article shows that when the observations are dependent, even slightly, the coverage probabilities of the usual confidence intervals can deviate noticeably from their nominal level. Several modified confidence intervals that incorporate the dependence structure are proposed and examined. Our results show that the modified Wilson, Agresti-Coull, and Jeffreys confidence intervals perform well and can be recommended for general use.
