Confidence Intervals by Repeated SamplingStatLens

Draw sample after sample from a population you choose. Each one gets the interval you would actually compute, x ± t*s/√n, and each dot is coloured by whether that interval caught μ. Hover a dot to see the sample behind it. Then hide μ, and watch what you would really have had.

Population:
Confidence:
Samples

Population where the samples come from

One sample the latest draw

Sampling distribution one dot per sample — hover one to see its interval

Press Hide μ. The colours go, and so does the count — because without μ nobody can say which intervals worked. That is the situation you are actually in: one sample, one interval, and no way to check it.

Confidence Intervals by Repeated Sampling — Help

The Sampling Distribution Lab's three tiers — population, one sample, the distribution of the statistic — with one addition: every sample gets a confidence interval, and every dot is coloured by whether that interval caught μ.

“But I only get one sample.” Quite. Press Hide μ: the colours vanish and the count disappears, because without μ nothing can tell which intervals worked — not the page, and not you. That is the real situation. Press Reveal and they snap back: your interval was one colour or the other all along, and hiding μ never changed which. It only removed your ability to see it, which is why the 95% has to be a claim about the method rather than about your interval.

CI Coverage makes the same count with a stack of interval bars instead of a distribution; Why the Percentile CI Works asks why a bootstrap may stand in for this sampling at all; Why ± 2 SE Works is the argument with no numbers.

Instructors: there is a printable guide, ?parameter=hidden opens with μ already hidden, and ?mode=present hides the student prompt.

Keyboard