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The problems of constructing confidence intervals (CIs) for the proportions and functions of proportions in finite populations are considered. For estimating the proportion in a finite population, we propose a CI based on the generalized fiducial method and compare it with an exact CI and score CI. For the two-sample problems, we consider interval estimating the difference between two proportions, the ratio of two proportions and the ratio of odds. Our solutions for the two-sample problems are based on the fiducial approach and the method of variance estimate recovery. All the CIs are evaluated on the basis of their exact coverage probabilities and expected widths. The methods are illustrated using some practical examples.

Fiducial confidence intervals for proportions in finite populations: One- and two-sample problems