Watch 100 confidence intervals

A 95% confidence interval doesn't promise that this interval contains the truth — it promises that the recipe catches the true mean about 95% of the time. Here you can watch that happen. We treat a whole real dataset as the population (so we know the true mean \(\mu\)), draw 100 samples, and build an interval from each:

\[ \bar{x} \;\pm\; t^{*}\,\frac{s}{\sqrt{n}} \]

Teal solid intervals (●) caught \(\mu\); orange-red dashed ones (✕) missed. Drag the sliders and draw fresh samples — does the hit rate track the confidence level?

Try it: shrink n toward 5 — intervals get wider (and a touch less reliable on skewed data). Raise the confidence level — the net widens to catch more. The miss rate should hover near (100 − level)%, no matter the sample.