Statistical Intervals for a Normal Population, Part II. Formulas, Assumptions, Some Derivations

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Abstract
The first part of this article, which was published in the July 1970 issue of the Journal of Quality Technology, described different types of confidence intervals, tolerance intervals, and prediction intervals; provided factors for constructing such intervals for a normal population; illustrated the calculation of the intervals; and compared their applications. This second, and final, part of the article indicates how the tabulated factors were obtained, examines the effect on the length of the intervals of increasing the sample size, reviews the importance of the normality assumption, briefly describes various additional intervals for a normal population, and provides information about a time-sharing computer program for obtaining statistical intervals. The mathematical basis for two of the intervals is given in two appendices, and a third appendix describes the construction of a confidence interval on a percentile of a normal distribution.