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Inference for Means

7

Introduction

We began our study of data analysis in Chapter 1 by learning graphical and numerical tools for describing the distribution of a single variable and for comparing several distributions. Our study of the practice of statistical inference begins in the same way, with inference about a single distribution and comparison of two distributions. Comparing more than two distributions requires more elaborate methods, which are presented in Chapters 12 and 13.

Two important aspects of any distribution are its center and spread. If the distribution is Normal, we describe its center by the mean and its spread by the standard deviation .

In this chapter, we will meet confidence intervals and significance tests for inference about a population mean and the difference between two population means . Chapter 6 emphasized the reasoning of significance tests and confidence intervals; now we emphasize statistical practice and no longer assume that population standard deviations are known. As a result, we move away from the standard Normal sampling distribution to a new family of distributions. The procedures for inference about means are among the most commonly used statistical methods.