Confidence Intervals — What 95% Really Means
Display 100 confidence intervals to clear up the classic 95% misreading. Slide the confidence level and watch the coverage rate change — experimentally, not just in theory.
I.03 / CONFIDENCE INTERVAL
Confidence Interval
LLN says "at infinity, you're right." But in practice we always have a finite sample. So instead of a single point, drape a net around it — that's a confidence interval. Wider net, easier to catch; narrower, more precise. Watch the trade-off play out.
The 95% confidence interval is famously misunderstood.
It does NOT mean "the true value is inside with 95% probability". The correct reading:
"repeat this sampling many times, and ~95% of the resulting intervals will capture the true value".
The lab below brute-forces that intuition. Thin pink = the unlucky intervals that missed.
Once the pink share settles around ~5%, you've got it.
x̄ ± zα/2 · σ/√n
Intervals built0
Coverage—
Expected95%