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. With samples of various sizes, the empirical sampling distribution of the simple expansion estimator was remarkably symmetric and approximately normal, as was that of the customary ratio-of-means estimator. While the nominal coverage rate of (1 - alpha)100% intervals based on the Student's t distribution was nearly achieved in all cases, there was a substantially greater tendency for such intervals to fail from below rather than above. This behavior is attributed to the strong positive correlation between the estimator of the population total and the corresponding estimator of its variance when sampling from a finite, and perforce nonnormal, population.