Sampling Distribution and Parameter Estimation

Abstract

This chapter begins with a discussion on the sample statistics and their sampling distributions, followed by the estimation of population parameters, including point estimation and interval estimation. It discusses the sampling distributions of several commonly used statistics because they play an important role in statistical inference. The central limit theorem is the mathematical theorem that gives the relationship between the sampling distribution of the sample mean and population mean. The chapter demonstrates a method for characterizing the sampling distributions of the sample mean and variance for continuous variables. There are two types of estimation of population parameters: point estimation and interval estimation. Several commonly used statistics and their expansions are estimated by point estimation and interval estimation for the corresponding population parameters. Confidence interval establishes a range of values using sample statistics and its standard error, with a predefined confidence level to comprehensively support the parameter estimation.