TAILIEUCHUNG - Ebook Probability and statistics for engineers and scientists (4th edition): Part 2
(BQ) Part 2 book "Probability and statistics for engineers and scientists" has contents: Hypothesis testing, regression, analysis of variance, goodness of fit tests and categorical data analysis, nonparametric hypothesis tests, quality control, life testing, simulation, bootstrap statistical methods, and permutation tests. | Chapter 8 HYPOTHESIS TESTING INTRODUCTION As in the previous chapter, let us suppose that a random sample from a population distribution, specified except for a vector of unknown parameters, is to be observed. However, rather than wishing to explicitly estimate the unknown parameters, let us now suppose that we are primarily concerned with using the resulting sample to test some particular hypothesis concerning them. As an illustration, suppose that a construction firm has just purchased a large supply of cables that have been guaranteed to have an average breaking strength of at least 7,000 psi. To verify this claim, the firm has decided to take a random sample of 10 of these cables to determine their breaking strengths. They will then use the result of this experiment to ascertain whether or not they accept the cable manufacturer’s hypothesis that the population mean is at least 7,000 pounds per square inch. A statistical hypothesis is usually a statement about a set of parameters of a population distribution. It is called a hypothesis because it is not known whether or not it is true. A primary problem is to develop a procedure for determining whether or not the values of a random sample from this population are consistent with the hypothesis. For instance, consider a particular normally distributed population having an unknown mean value θ and known variance 1. The statement “θ is less than 1” is a statistical hypothesis that we could try to test by observing a random sample from this population. If the random sample is deemed to be consistent with the hypothesis under consideration, we say that the hypothesis has been “accepted”; otherwise we say that it has been “rejected.” Note that in accepting a given hypothesis we are not actually claiming that it is true but rather we are saying that the resulting data appear to be consistent with it. For instance, in the case of a normal (θ, 1) population, if a resulting sample of size 10 has an average value of .
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