Statistics and Probability with Applications for Engineers and Scientists, Preliminary Edition

Chapter 7

Sampling Distributions

The focus of this chapter is a discussion of sampling distributions of functions of random variables. The topics covered are:

• Basic concepts of sampling from both an infinite and finite population
• Distributions of the sample average and sample proportion
• A fundamental theorem of probability known as the Central Limit Theorem
• Distributions related to the normal distribution, namely, chi-square, Student t, and Snedecor's F distributions, that are very useful in applied statistics
• Distributions of various order statistics, and their applications
• The use of different statistical packages, MINITAB, Microsoft Excel, and JMP

Learning Outcomes

After studying this chapter, the reader will be able to

• Understand the basic concepts of sampling distributions.
• Understand the Central Limit Theorem and when to apply it.
• Understand the details of important sampling distributions, namely chi-square, Student t, and Snedecor's F distributions, and use them to draw conclusions about problems that arise in applied statistics.
• Develop the distributions of various order statistics.
• Use MINITAB, Microsoft Excel, and JMP in areas of applied statistics.

7.1 Random Sampling

In this chapter we study topics that build a foundation for what is called inferential Statistics. In inferential statistics we use the information contained in a random sample to make predictions about the population from which the sample has been drawn. In Chapter 2 we gave a very brief discussion ...