08 — Confidence Intervals

CI = x̄ ± z · (σ/√n) · ● dot = sample mean · line = full interval. Across many samples, ~95% catch the true μ.

A. The population — N(μ=50, σ=15) with one sample drawn

B. Sample mean & 95% CI — built from that sample

C. Run 100 experiments

Caught0

Missed0

Coverage—

caught true μ missed dot = sample mean line = full interval [lo, hi]

Confidence level: 95%

Sample size n: 30

Watch out: the interval is random, not μ. Say "the procedure catches μ 95% of the time" — not "there's a 95% chance μ is here."