# ch01 - \$ STAT 401 Experimental Methods 1 Ch.1 Introduction...

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STAT 401: Experimental Methods 1 Ch.1: Introduction 1.1 Statistics and Engineering Statistics deals with collecting, processing, summarizing, analyzing and interpreting data. On the other hand, engineering and industrial management deal with such diverse issues as solving production problems, effective use of materials and labor, development of new products, quality improvement and reliability and, of course, basic research. The usefulness of statistics as a tool for dealing with the above problems is best seen by considering some examples of specific engineering tasks: 1. estimating the coefficient of thermal expansion of a metal, 2. comparing the hardness of two or more cement mixtures,

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3. comparing the effectiveness of three cleaning products in removing four different types of stains, 4. predicting failure time on the basis of stress applied, 5. studying the relation between vibrations of high-speed train tracks and speed of the train, 6. assessing the effectiveness of a new traffic regulatory measure in reducing the weekly rate of accidents, 7. testing a manufacturer’s claim regarding the quality of his/her product, 8. studying the relation between salary increases and employee productivity in a large corporation, 9. estimating the proportion of the US citizens of age 18 and over who are in favor of expanding solar energy sources, and 10. determining whether the content of lead in the water of a certain lake is within the safety limit.
The reason why tasks like the above require statistics is variability . Thus, if the hardness of all preparations of the same cement mixture were the same, the task of comparing the hardness of two cement mixtures of example 2 would not require statistics; it would suffice to compare the hardness of one preparation from each of the two cement mixtures. However, the hardness of different preparations of the same cement mixture (even when done by the same preparer) will differ, complicating thus the said comparison problem. An appreciation of the complications caused by variability begins by realizing that the problem of task 2, as stated, is ambiguous. Indeed, if the hardness of preparations of the same cement mixture differ, then what is meant by comparing the hardness of different cement mixtures? A more precise statement of the problem would be to compare the average or mean hardness of the different cement mixtures. (A similar comment applies to the other aforementioned examples except to example 4 on prediction.) Moreover, the familiar

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words of average and mean have a technical meaning in statistics, and full understanding of it requires a clear distinction between the concepts of population and sample. These concepts are discussed in the next subsection. In summary, Statistics is an indispensable tool for dealing with the variability which is inherent in many (if not most) engineering and scientific studies.
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