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

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9

Hypothesis Testing

. . .the null hypothesis is never proved or established, but is possibly disproved, in the course of experimentation. Every experiment may be said to exist only to give the facts a chance of disproving the null hypothesis.

R. A. Fisher

The focus of this chapter is a discussion of testing of statistical hypotheses.

Topics Covered:

  • Basic concepts of testing of statistical hypotheses
  • Tests concerning the mean of a normal distribution when variance is known
  • Tests concerning the mean of a normal distribution when variance is unknown
  • Tests concerning population means when sample size is large
  • Tests concerning the difference of means of two populations with known variances
  • Tests concerning the difference of means of two populations with unknown variances
  • The paired t-test
  • Testing concerning one and two population proportions when sample size is large
  • Tests concerning the variance of a normal distribution
  • Tests concerning the ratio of variances of two normal populations
  • Sequential tests of hypotheses

Learning Outcomes:

After studying this chapter, the reader will be able to

  • Construct null and alternative hypotheses.
  • Determine an appropriate test statistic and use it to carry out a hypothesis test.
  • Understand the concepts of type I and type II errors, and determine the power of a test
  • Understand the concept of the p-value, calculate it, and then use it to make the correct decision.
  • Use appropriate confidence intervals to carry out various tests of hypotheses.

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