Statistics and Probability with Applications for Engineers and Scientists Using MINITAB, R and JMP, 2nd Edition

Chapter 9Hypothesis 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 the 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 the 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. ...