The paper considers the sample survey type problem of estimating the proportion p of a finite population of size N having a given attribute by the proportion of successes in a random sample (with or without replacement) of size r from the population. The present main result indicates that is always at least a 91.0% confidence interval (C.I.) for the parameter p. The paper shows that is at least as large under the hypergeometric model of simple random sampling without replacement as it is under the corresponding binomial model of random sampling with replacement. The significance of the present main result is that it is a good, easily stated accuracy rule, holding for all r,N, and p, which can easily be understood by the layman when assessing accuracy of the estimator and discussing the relationship between accuracy and áwhen assessing accuracy of the estimator and discussing the relationship between accuracy and sample size.
