II. Probability and Statistics for Reliability
B. Statistical inference
3. Hypothesis testing (parametric and non-parametric) (Evaluate)
Apply hypothesis testing for parameters such as means, variance, proportions, and distribution parameters. Interpret significance levels and Type I and Type II errors for accepting/rejecting the null hypothesis.
The testing of measures of dispersion is as simple as comparing means.
Additional References
Hypothesis Tests for Variance Case I (article)
Hypothesis Tests for Variance Case II (article)
Quick Quiz
This Chi-square test is for variance against an known historical variance parameter, I wonder why you establish the null and alternative as “means”
Yep, good catch Maria. the mu’s in the setup of the hypothesis test should be sigma squared (variance). cheers, Fred
Can you review the conclusions of the example provided in which a process has a target of 4 sigma = 60? If samples resulted in a lower standard deviation of 12 how came do not meet the requirement of sigma =15? For me it doesn’t make sense
Hi Maria,
The sample we have used for the calculated stdev of 12 is a sample, it is not the actual stdev… there is uncertainty around that value. The chi-sq’d test based in part on the degrees of freedom estimates that range of uncertainity and in this case concludes that the sample stdev of 12 is not statistically significantly different than the target of 15. The process we pulled the samples from may or may not have a lower stdev then 15. We do not have enough data to be sure.
cheers,
Fred