Hypothesis tests
Hypothesis tests
- A hypothesis test uses sample data to judge a claim.
- the null hypothesis $H_0$ — the claim (usually "no change"); the alternative $H_1$ — what you suspect.
- one-tailed if $H_1$ points one way ($\mu > 50$); two-tailed if both ($\mu \neq 50$).
Practice
The null hypothesis H₀ usually states that:
H₀ is the claim being tested, usually "no change"; H₁ is the suspected alternative.
Running the test
- Fix a significance level (often 5%), compute a test statistic, and see if it lands in the rejection region.
$$z = \frac{\bar{x} - \mu}{\sigma/\sqrt{n}}$$
- Type I error: rejecting $H_0$ when it is true. Type II error: accepting $H_0$ when it is false.
Practice
Population mean claimed 50, σ = 8, sample n = 64, x̄ = 52. What is z = (x̄ − μ)/(σ/√n)?
z = (52 − 50)/(8/√64) = 2/(8/8) = 2/1 = 2.
Practice
A Type I error is:
Type I = reject a true H₀; Type II = accept a false H₀.
You've got it
Key idea
- $H_0$ (no change) vs $H_1$ (suspected); one- or two-tailed
- test statistic $z = \dfrac{\bar{x} - \mu}{\sigma/\sqrt{n}}$; reject $H_0$ if it's in the rejection region
- Type I = reject a true $H_0$; Type II = accept a false $H_0$