Confidence Interval Lab
Skill goal: See what “95% confident” really means by simulating 100 intervals and counting how many capture the true mean.
1 · Observe
Each horizontal segment is one interval. Green captured the true mean μ = 50; red missed it.
2 · Manipulate
3 · Predict
Before simulating at 95%: out of 100 intervals, about how many will miss the true mean? Now switch to 99% — will the intervals get wider or narrower?
4 · See
5 · Explain
A 95% confidence interval is built as x̄ ± z*·σ/√n. The 95% describes the method, not one interval: if we repeat the process forever, about 95% of the intervals trap μ. Higher confidence needs a bigger z* (wider net); bigger n shrinks the standard error (tighter net).
6 · Challenge
Q: Raising the confidence level from 95% to 99% makes each interval…