Engineering statistics statistical hypothesis testing

There are many cases in which a scientist or an engineer needs to compare the mean of a data set with a known value. In some cases, the known value is the true or accepted value based on prior knowledge or experience. In other situations, the known value might be a value predicted from theory or it might be a threshold value that we use in making decisions about the presence or absence of a constituent. In all these cases, we use a statistical hypothesis test to draw conclusions about the population mean y. and its nearness to the known value, which we call p.Q. 

Fora discussion of errors hypothesis testing, see J. L. Devore. Proha-bilily and Statistics for Engineering and the Sciences. 6th ed., Chap. 8, Pacific Grove. CA Duxbury Press at Brooks/Cole, 20()4. 

The basis for any statistical analysis is the fact that all data are to some extent, one way or another, subject to chance errors. These chance errors may arise whether the problem involves an estimation, the development of a reliable model, or the testing of a hypothesis. For example, since no experimentally determined value in the laboratory is absolute, it is generally necessary to determine by statistical analysis the reliability of the newly obtained data, The eventual use of these data by the engineer in design work may often determine the necessary confidence level that will be required concerning the true value of the data. 

The critical value for this test is given by Z, j = Zo 25 = 1-96. Hence, there is no statistical evidence to support the rejection of the nuU hypothesis, and the proper decision would be to purchase both weUs under the management interpretation of these results. However, the same clever engineer who questioned the first test results again questioned the validity of using o-j and al in the calculations. The question was then posed, Can we perform a similar test without knowing the population variances The statistician responded yes as the same example used to calculate Xj and X2 could be used to estimate erf and erf with Sj and SI, respectively. 

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