Two topics are investigated in this dissertation. The first concerns variance estimation when a single primary sampling unit is selected. Two new bias variance estimators, based on splitting the initial sample into sub-samples and regarding the initial sample as a stratified sample, are proposed. The results of this study indicated that both new variance estimators are underestimated. The first variance estimator is not preferable when the number of sub-samples is two because its relative bias is too large to be useful. Increasing the number of ...