Statistical Inference: A Short Course

11.1 Confidence Intervals for the Difference of Means when Sampling from Two Independent Normal Populations

Let and be random samples taken from independent normal distributions with means and and variances and , respectively. Our goal is to obtain a 100(1 − α)% confidence interval for the difference of means . To accomplish this task, we must first examine the properties of the sampling distribution of the difference between two sample means.

Suppose X and Y are independent random variables, where X is and Y is . For to serve as an estimator for , we need to study the properties of the distribution ...