CHAPTER 9 Tests of Hypotheses for a Single Sample by Douglas C. Montgomery, George C. Runger

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INTRODUCTION

In the previous two chapters we showed how a parameter of a population can be estimated from sample data, using either a point estimate (Chapter 7) or an interval of likely values called a confidence interval (Chapter 8). In many situations a different type of problem is of interest; there are two competing claims about the value of a parameter, and the engineer must determine which claim is correct. For example, suppose that an engineer is designing an air crew escape system that consists of an ejection seat and a rocket motor that powers the seat. The rocket motor contains a propellant, and in order for the ejection seat to function properly, the propellant should have a mean burning rate of 50 cm/sec. If the burning rate is too low, the ejection seat may not function properly, leading to an unsafe ejection and possible injury of the pilot. Higher burning rates may imply instability in the propellant or an ejection seat that is too powerful, again leading to possible pilot injury. So the practical engineering question that must be answered is: Does the mean burning rate of the propellant equal 50 cm/sec, or is it some other value (either higher or lower)? This type of question can be answered using a statistical technique called hypothesis testing. This chapter focuses on the basic principles of hypothesis testing and provides techniques for solving the most common ...

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