Statistics, as the science of drawing meaningful conclusions about populations from representative samples, employs various sampling techniques, including simple, stratified, systematic, and cluster random sampling. The choice of sampling method hinges on research objectives, available population information, and budget constraints. From these samples, valuable insights into population parameters are derived, with a focus on mean (μ), proportion (p), variance (σ²), and total (τ). Additionally, the population size (N) serves as a crucial yet less common parameter.
In the context of finite populations, estimating these parameters and their variances relies on a known value for N. However, when N is unknown, it becomes necessary to estimate it beforehand to accurately assess population totals and estimator variances.
This paper delves into the intricacies of statistics, emphasizing the significance of appropriate sampling techniques and parameter estimation, particularly in scenarios where the population size remains uncertain