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Statistics and Probability with Applications for Engineers and Scientists by Irwin Guttman, Bhisham C. Gupta

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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 ...

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