Statistics for Environmental Engineers

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The choice of a statistical interval depends on the application and the needs of the problem. One must decide whether the main interest is in describing the population or process from which the sample has been selected or in predicting the results of a future sample from the same population. Confidence intervals enclose the population mean and tolerance intervals contain a specified proportion of a population. In contrast, intervals for a future sample mean and intervals to include all of m future observations are called prediction intervals because they deal with predicting (or containing) the results of a future sample from a previously sampled population (Hahn and Meeker, 1991).

Confidence intervals were discussed in previous chapters. This chapter briefly considers tolerance intervals and prediction intervals.

Tolerance Intervals

A tolerance interval contains a specified proportion (p) of the units from the sampled population or process. For example, based upon a past sample of copper concentration measurements in sludge, we might wish to compute an interval to contain, with a specified degree of confidence, the concentration of at least 90% of the copper concentrations from the sampled process. The tolerance interval is constructed from the data using two coefficients, the coverage and the tolerance coefficient. The coverage is the proportion of the population (p) that an interval is supposed to contain. The tolerance coefficient is the degree of confidence with which the interval reaches the specified coverage. A tolerance interval with coverage of 95% and a tolerance coefficient of 90% will contain 95% of the population distribution with a confidence of 90%.

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