🟢 Stats: Confidence Intervals — What They Really Mean
CI = x̄ ± z × (σ/√n)
z-values: 90% → 1.645, 95% → 1.96, 99% → 2.576
What 95% CI means: "If we repeated this experiment 100 times, about 95 of the resulting intervals would contain the true population parameter."
What it does NOT mean: "There's a 95% probability the true value is in this interval." The true value is fixed — it either is or isn't. The confidence is about the procedure.
For proportions: CI = p̂ ± z × √[p̂(1-p̂)/n]
Practice Questions
Q: Sample mean = 50, SD = 12, n = 36. What's the 95% CI?