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.
Here is a simple process to use when comparing a datasets to a standard or another dataset.
Additional References
Hypothesis Testing (article)
Run Test for Randomness (article)
Hypothesis Test Selection (article)
Hypothesis Test Selection Flowchart (article)
Hypothesis Test Sample Size (article)
Quick Quiz
1-26. The level of significance is defined as the probability of which of the following?
(A) accepting a null hypothesis when it is true
(B) not accepting a null hypothesis when it is true
(C) rejecting a null hypothesis when it is true
(D) not rejecting a null hypothesis when it is true
(C) rejecting a null hypothesis when it is true
The null hypothesis is rejected if the p-value is less than the significance or α level. The α level is the probability of rejecting the null hypothesis given that it is true (type I error).
The null hypothesis is a statement about a belief. We may doubt that the null hypothesis is true, which might be why we are “testing” it. The alternative hypothesis might, in fact, be what we believe to be true. The test procedure is constructed so that the risk of rejecting the null hypothesis, when it is in fact true, is small. This risk, α is often referred to as the significance level of the test. By having a test with a small value of α, we feel that we have actually “proved” something when we reject the null hypothesis. (NIST Engineering Statistical Handbook)
1-37. Which term is commonly used as the probability of rejecting material produced at an unacceptable quality level?
(A) α
(B) β
(C) 1 − α
(D) 1 − β
(D) 1 − β
β is the probability of accepting the lot or batch when we shouldn’t. It is the chance of a false acceptance given the sample data when the population would not be acceptable. Therefore the meaning of 1 − β is the probability of rejecting (properly so) an unacceptable lot of material. The sample indicates the population is bad and it is bad.
1 − β is also known as the power of the test which means the ability to sample to detect a unacceptable population. β is also called the Type II error or consumer’s risk. In contract, α is the Type I error or producer’s risk.
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