Sampling-skewed biological populations: Behavior of confidence intervals for the population total

Four populations were repeatedly sampled with the aim of examining interval estimation of the cumulative amount, T, of some characteristic that has a positively skewed distribution, a feature of many biological populations. W ith samples of various sizes, the empirical sampling distribution of the si mple expansion estimator was remarkably symmetric and approximately normal, as was that of the customary ratio-of-means estimator. While the nominal c overage rate of (1 - alpha)100% intervals based on the Student's t distribu tion was nearly achieved in all cases, there was a substantially greater te ndency for such intervals to fail from below rather than above. This behavi or is attributed to the strong positive correlation between the estimator o f the population total and the corresponding estimator of its variance when sampling from a finite, and perforce nonnormal, population.