Hypothesis testing

Probability of Type I error you'll accept. Standard: 5% or 1%.

Two ways to make the same decision. p-value is the probability of an outcome as extreme as observed under H0.

Set H₀ and H₁. Calculate p-value. Reject H₀ if p < significance level.

Y12 (binomial), Y13 (normal, correlation). Process: state hypotheses, choose significance level, calculate test statistic and p-value, conclude.

Worked examples

Coin biased? H₀: p = 0.5; H₁: p > 0.5. 30 flips, 20 heads. Under H₀: P(X ≥ 20|p=0.5) ≈ 0.0214 < 0.05; reject.

Two-tailed at 5%: critical region is the most-extreme 2.5% in each tail.

Type I error: reject true H₀. Type II: accept false H₀.

Frequently asked questions

Significance level?

Probability of Type I error you'll accept. Standard: 5% or 1%.

p-value vs critical region?

Two ways to make the same decision. p-value is the probability of an outcome as extreme as observed under H₀.