Distribution of sample means and confidence intervals for μ

What this note covers

1. Why sample means vary: intuition before the theorem
2. The Central Limit Theorem: statement and conditions
3. Standard error and its practical meaning
4. Confidence intervals for μ with known σ
5. Confidence intervals for μ with unknown σ — using s as an estimate
6. Determining the required sample size
7. Connecting the CLT, confidence intervals, and real decisions

7 sections · 12 key terms & formulas · 6 common mistakes