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📏 Confidence Intervals, the Z-Test, and What "Coverage" Really Means

What a 95% confidence interval actually promises, how the Z-test uses the same machinery to test a hypothesis, and why both tools rely entirely on the Central Limit Theorem underneath.

Statistics3DAdvanced60 FPS

Draw repeated random samples and watch confidence intervals stack up as bars along a depth axis — green when they capture the true mean, red when they miss — while a linked Z-test scores the latest sample against a hypothesized value.

🔬 What It Demonstrates

Coverage is a long-run property of the interval-building procedure: roughly C% of intervals built this way capture μ over many repeats, exactly as the accumulating green/red bars and running coverage percentage show.

🎮 How to Use

Adjust sample size, confidence level, population spread, and the Z-test's hypothesized mean, then draw samples one at a time or in a batch of 20 to watch the sampling distribution and coverage rate respond.

💡 Did You Know?

A 95% CI does not mean "95% probability μ is in this interval" — once computed, an interval either contains μ or it doesn't. The 95% describes the procedure's long-run behaviour, which this simulation lets you watch directly.

⚙ Under the hood

What a 95% confidence interval actually promises, how the Z-test uses the same machinery to test a hypothesis, and why both tools rely entirely on the Central Limit Theorem underneath.

probabilityconfidence intervalshypothesis testingz-testcentral limit theoremdata analysisThree.js

3D · Three.js / WebGL renderer · 60 FPS target · runs fully client-side, no install