Statistics from Simulations A.1 Statistical Inference and Estimation of Population Parameters

When the goal is to estimate the parameter of some population (e.g., mean or variance), the usual procedure is to design a probability sample to provide a sample statistic. As an example, we might estimate the parameter ‘true average cost’ of an inventory system (population mean, ) with the statistic ‘average cost for 12 months’ (sample mean, x ); or we might estimate the proportion of taxpayers whose income tax returns were audited by the IRS in a particular year (population proportion, ) by using the proportion of a random sample that were audited (sample proportion, p). When a single number based on a sample is used to estimate the population parameter ( x for or p for ), it is termed a point estimate. While such estimates are indispensable for calibrating a model, they provide no insight into the extent of random sampling error. Interval estimates, on the other hand, allow us to specify the maximum expected error and associated probability that a point estimate would diverge from the population parameter.