Optimal sampling strategies which minimize the expected mean square error for a linear unbiased estimator,model and model-design unbiased estimators for expected finite population mean,are obtained under a correlated superpopulation model. This is found, when the parent infinite superpopulation assumed to be distributed as a multivariate normal distribution, the Pearsonian kurtosis coefficient of the sample mean based on distinct units, defined by Koop (1986) is always greater than three, unless the sample is based on a fixed effective sample size design.
