In a weighted sample, not all sample observations contribute equally to the estimate of a population parameter.
Investigators are often interested in estimating quantities (such as means, counts, or proportions) in a population by using a representative sample selected from that population. Probability samples, defined as samples in which each sampling unit has a known, nonzero probability of selection based on the sampling design, allow investigators to compute estimates of population parameters. The most straightforward type of probability sampling design, a simple random sample (SRS), is a selection method in which each sample has the same probability of being selected. In an SRS, the probability of selection of each member in the population is the same.
The estimation of the population mean is straightforward for the SRS design. Let n = sample size, N = population size. Also, let \( \< , \ldots, \> \) be the population values and \( \< , \ldots, \> \) .
