Continuous Probability Distributions, Confidence Intervals, and Hypothesis Testing

Edward B. Magrab
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Edward B. Magrab: University of Maryland

Chapter Chapter 2 in Engineering Statistics, 2022, pp 29-91 from Springer

Abstract: Abstract In this chapter, we introduce continuous probability density functions: normal, lognormal, chi square, student t, f distribution, and Weibull. These probability density functions are then used to obtain the confidence intervals at a specified confidence level for the mean, differences in means, variance, ratio of variances, and difference in means for paired samples. These results are then extended to hypothesis testing where the p-value is introduced and the type I and type II errors are defined. The use of operating characteristic (OC) curves to determine the magnitude of these errors is illustrated. Also introduced is a procedure to obtain probability plots for the normal distribution as a visual means to confirm the normality assumption for data.

Date: 2022
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DOI: 10.1007/978-3-031-05010-7_2

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