7

Sampling Distributions

# The focus of this chapter is to discuss sampling distributions of functions of random variables

# Topics Covered

- 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, which are very useful in applied statistics
- Distributions of various order statistics, and their applications
- Use of different statistical packages, namely 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 make conclusions about problems that arise in applied statistics.
- Develop the distributions of various order statistics.
- Make use of 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 had a very brief discussion about various ...