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Statistical Inference: A Short Course by Michael J. Panik

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

Let img and img be random samples taken from independent normal distributions with means img and img and variances img and img, respectively. Our goal is to obtain a 100(1 − α)% confidence interval for the difference of means img. 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 img and Y is img. For to serve as an estimator for , we need to study the properties of the distribution ...

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