Optimal hypergeometric confidence sets are (almost) always intervals

We present an efficient method of calculating exact confidence intervals for the hypergeometric parameter. The method inverts minimum-width acceptance intervals after shifting them to make their endpoints nondecreasing while preserving their level. The resulting set of confidence intervals achieves minimum possible average width, and even in comparison with confidence sets not required to be intervals it attains the minimum possible cardinality most of the time, and always within 1. The method compares favorably with existing methods not only in the size of the intervals but also in the time required to compute them. The available R package hyperMCI implements the proposed method.