ABSTRACT
Chapter 3 introduces probability distributions for statistics, which are called sampling distributions. These enable us to evaluate how precisely statistics estimate population parameters. We discuss in more detail the sampling distribution of sample means and present the law of large numbers which states that the sample mean converges to the population mean as the sample size increases. We also introduce the Central Limit Theorem, a remarkable result stating that with studies employing randomization, the sample mean has approximately a normal sampling distribution. We finally show by the delta method that sampling distributions of many statistics other than the sample mean are also approximately normal.
