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Ebook Probability & statistics for engineers & scientists (9/E): Part 2

(BQ) Part 2 book “Probability & statistics for engineers & scientists” has contents: Simple linear regression and correlation, multiple linear regression and certain nonlinear regression models, factorial experiments, nonparametric statistics, and other contents. | www.downloadslide.net Chapter 10 One- and Two-Sample Tests of Hypotheses 10.1 Statistical Hypotheses: General Concepts Often, the problem confronting the scientist or engineer is not so much the estimation of a population parameter, as discussed in Chapter 9, but rather the formation of a data-based decision procedure that can produce a conclusion about some scientific system. For example, a medical researcher may decide on the basis of experimental evidence whether coffee drinking increases the risk of cancer in humans; an engineer might have to decide on the basis of sample data whether there is a difference between the accuracy of two kinds of gauges; or a sociologist might wish to collect appropriate data to enable him or her to decide whether a person’s blood type and eye color are independent variables. In each of these cases, the scientist or engineer postulates or conjectures something about a system. In addition, each must make use of experimental data and make a decision based on the data. In each case, the conjecture can be put in the form of a statistical hypothesis. Procedures that lead to the acceptance or rejection of statistical hypotheses such as these comprise a major area of statistical inference. First, let us define precisely what we mean by a statistical hypothesis. Definition 10.1: A statistical hypothesis is an assertion or conjecture concerning one or more populations. The truth or falsity of a statistical hypothesis is never known with absolute certainty unless we examine the entire population. This, of course, would be impractical in most situations. Instead, we take a random sample from the population of interest and use the data contained in this sample to provide evidence that either supports or does not support the hypothesis. Evidence from the sample that is inconsistent with the stated hypothesis leads to a rejection of the hypothesis. 339 340 Chapter 10 One- and Two-Sample Tests of Hypotheses www.downloadslide.net The Role of .