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Continuous Probability Distributions, Confidence Intervals, and Hypothesis Testing

In: Engineering Statistics

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  • Edward B. Magrab

    (University of Maryland)

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.

Suggested Citation

  • Edward B. Magrab, 2022. "Continuous Probability Distributions, Confidence Intervals, and Hypothesis Testing," Springer Books, in: Engineering Statistics, chapter 0, pages 29-91, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-05010-7_2
    DOI: 10.1007/978-3-031-05010-7_2
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