A LARGER SAMPLE SIZE IS NOT ALWAYS BETTER!!!

In a previous paper Neerchal, Lacayo and Nussbaum (2007) explored the behavior of the well-known problem of finding the optimal sample size for obtaining a confidence interval of a pre-assigned precision (or length) for the proportion parameter of a finite or infinite binary population. We illustrated some special problems that arise due to the discreteness of the population distribution and precision that is measured by the length of the interval rather than by the variance. Specifically, the confidence level of an interval of fixed length does not necessarily increase as the sample size increases. However, when such confidence levels are computed using normal approximations, we see a monotonic behavior. In this paper, we consider the corresponding problem under the Poisson approximation and show that for this distribution monotonicity does not hold and one should be beware of this seeming peculiarity in recommending sample sizes for studies involving estimation of means or proportions