Cost Issue in Estimation of Proportion in a Finite Population Divided Among Two Strata

TL;DR

This paper examines how to optimally allocate samples between two strata in a finite population to minimize estimation variance within a budget, demonstrating potential variance reduction of up to 30%.

Contribution

It provides a method for optimal sample allocation in stratified sampling to improve estimation accuracy under budget constraints.

Findings

Optimal sample allocation can reduce variance by up to 30%.

Stratified sampling improves estimation efficiency over simple random sampling.

Budget constraints influence optimal sample size distribution.

Abstract

The problem of estimation of the proportion of units with a given attribute in a~finite population is considered. From the population a sample is drawn due to the simple random sampling without replacement. There are limited funds for conducting survey sample. Suppose that the population is divided into two strata. The question now arises: how should sample sizes be chosen from each strata to obtain the best estimation of proportion without exceeding the budget planned. In the paper it is shown, that with the appropriate sample allocation the variance of the stratified estimator may be reduced up to 30% off of the standard, unstratified estimator.