AdvancedTopic 86 of 104Engineering Mathematics
Hypothesis testing
Uses sample data to decide between competing claims while controlling error rates.
In depth
Define a null hypothesis H₀ and an alternative H₁, compute a test statistic, and compare the p-value with the significance level α. Type I error rejects a true H₀; Type II fails to reject a false one. Power is 1 minus the Type II rate.
Key points
- p-value is not the probability H₀ is true
- t-test, z-test, chi-square, ANOVA
- Control for multiple tests
ExampleTesting whether a new alloy has higher mean strength than the old one.
What is Hypothesis testing?
Uses sample data to decide between competing claims while controlling error rates.
Why is it important to understand hypothesis testing?
Hypothesis tests let you decide whether a change is real or just random variation, which prevents costly decisions based on noise.
What is a p-value?
It is the probability of seeing data at least as extreme as observed, assuming the null hypothesis is true. It is not the probability that the null hypothesis is true.
What is the difference between Type I and Type II errors?
A Type I error rejects a true null hypothesis, a false alarm. A Type II error fails to reject a false null hypothesis, a missed effect.
How is Hypothesis testing used in practice?
Typical applications include deciding if a new coating reduces corrosion rates in a trial, checking whether a supplier's parts meet a mean specification and comparing the vibration of two machine designs.
What should I learn before Hypothesis testing?
Study "Confidence intervals" first (topic 85 of 104 in Engineering Mathematics). It covers the groundwork this topic builds on.
What are the key points of Hypothesis testing?
p-value is not the probability H₀ is true. t-test, z-test, chi-square, ANOVA. Control for multiple tests.
Can you give an example of Hypothesis testing?
Testing whether a new alloy has higher mean strength than the old one.
What comes after Hypothesis testing?
The next topic is "Regression analysis", which builds directly on this one.
How difficult is Hypothesis testing?
It is classed as Advanced in Engineering Mathematics (topic 86 of 104). It is an advanced topic. It assumes you are comfortable with the intermediate topics in Engineering Mathematics.