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III. Reliability in Design and Development
II. B. 3. d. Hypothesis Testing – Comparisons
II. B. 3. c. Hypothesis Testing – Variance
II. B. 3. b. Hypothesis Testing – Means
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 first and simplest of hypothesis tests is with a mean compared to a specification or standard.
Additional References
Hypothesis Testing (article)
Hypothesis Tests for Proportion (article)
Degradation Hypothesis (article)
Quick Quiz
1-34. To compare sample means, which statistical distribution should be used?
(A) chi-square
(B) exponential
(C) normal
(D) t test
(D) t test
The key phrase here is “sample means”, thus the t-test is the best of the options. While the t-test is primarily for use with small samples —less then 30— drawn from normal populations it is fairly robust to non-normal populations for the comparison of means.
The exponential distribution is not used for the comparison of means using hypothesis testing. The normal or z-test is used to compare the population (not sample) means. The chi-square distribution is used to compare population variances or to compare the observed and expected frequencies of test outcome.
