How do I explore?

1. Pick a sample size and a confidence level.
2. Press Sample (or Sample 100) to draw samples from the population. Each sample builds one confidence interval on the right.
3. Press Clear plot to start over, or New population for a new true mean.

What should I notice?

• About what fraction of the intervals capture the true mean (the blue line)? How does it compare to the confidence level you chose?
• What happens to the width of the intervals when you make the sample size bigger? When you raise the confidence level?

Where is the data?

This sim is self-contained — the data is right here on the plot. Each confidence interval is one line, coloured by whether it captured the true mean (the blue line). The running “X of N capture (Z%)” at the top is the capture rate.

Primary standard

• HSS-IC.B.4 / AP Statistics (UNC-4) — interpret a confidence level as the long-run capture rate of the interval procedure.

Design intent

• The true mean is known and fixed, so students can see which intervals miss — something impossible with a single real sample. The confidence level sets the long-run capture rate, not the certainty of any one interval.
• Interval width responds to sample size (∝ 1/√n) and to the confidence level, so students feel the precision-versus-confidence trade-off directly.

Discussion prompts

• If 95% confidence gives about 95% capture, why can't we say a single interval has a 95% chance of containing μ?
• Why do higher-confidence intervals get wider, not narrower?

Suggested activity flow

• Observe first: draw a few samples one at a time; predict, then check whether each captures μ.
• Then Sample 100 and read the capture rate. Change the sample size and the confidence level and predict the effect before you test it.

Assumptions and simplifications

• Samples are drawn from a normal population; each interval is x̄ ± t*·s/√n with t* for the chosen level and n − 1 degrees of freedom.