Lab 03 / Uncertainty
What 95% covers
Does every 95% interval contain the true value?
Generate many intervals from one fixed synthetic population and count how often the method captures its known mean. Change one control at a time, then open the values under the chart before interpreting the picture.
View the values behind this chart
Loading the deterministic simulation...
SEEDInterpret the result
The paired guide explains the mechanism, assumptions, and cases where this display should not be generalized.
What this display answers
A confidence level belongs to a procedure used repeatedly. Some individual intervals miss the fixed population mean even when every assumption is exactly satisfied.
Changing the seed changes which intervals miss. Raising the confidence level widens every interval and usually increases coverage; increasing sample size narrows intervals while preserving the target long-run rate.
What to notice
- Look for coral intervals among the first 34 displayed draws.
- Compare the target confidence level with observed coverage over 200 draws, then increase repetitions to reduce simulation noise.
- Switch from 90% to 99% and watch the margin widen.
The model behind it
The experiment draws independent normal observations with known population standard deviation 10 and fixed mean 50. It therefore uses a z interval, not an estimated-sigma t interval.
Known sigma is intentionally artificial: it makes the repeated-coverage mechanism visible without mixing in another approximation.
Where the result stops
Once an interval has been computed in this frequentist model, the fixed parameter is not randomly moving in and out of it.
Biased sampling, dependence, data-dependent stopping, or a mismatched interval procedure can make nominal coverage misleading.