Chapter 9 - Statistical Inferences for the Mean: This chapter requires a good knowledge of Chapter 7. Some parts require a knowledge of sections 8.3 and 8.4

Abstract

This chapter is concerned with statistical inferences for the mean. The ideas, approaches, and nomenclature concerning statistical inference developed will mostly be applicable to the other quantities. Statistical inferences for the mean can be divided into two main categories. In one category, the variance or standard deviation of the population and the normal distribution can be used for calculations. In the other category, an estimate of the variance or a standard deviation of the population from the sample itself can be found. The normal distribution is assumed to apply to the underlying population, but another distribution related to it will usually be required for calculations. This chapter discusses in detail the inferences for the mean when variance is known. It explains the test of hypothesis and confidence interval and describes the inferences for the mean when variance is estimated from a sample. It also explores the confidence interval using the t-distribution, comparing a sample mean to a population mean, a comparison of sample means using unpaired samples, and a comparison of paired samples.