Probability
Confidence Intervals
What a 95% confidence level actually means across repeated experiments
50 experiments
Key ideas
- A 95% CI does not mean there's a 95% chance $\mu$ is inside this interval. $\mu$ is fixed.
- It means: if you repeat the experiment many times, ~95% of intervals will capture $\mu$.
- Larger n $\to$ narrower intervals (more precise), same coverage rate.
- Higher confidence $\to$ wider intervals (less precise), fewer misses.