How do I simulate a sampling error?

Open this page and use the live Confidence Intervals tool below — set your inputs and the simulation runs instantly in your browser using real numerics. No install, no account needed.

Yes. The simulation runs free in your browser. A one-time unlock or a Pro plan adds advanced parameters, saved presets, data import, and clean exports.

Can I use my own numbers?

Absolutely — every input is adjustable, and with data import you can drive a sampling error from your own measurements.

Use case · powered by Confidence Intervals

Confidence Intervals for a sampling error

Simulate a sampling error live in your browser. This runs the real Confidence Intervals solver — adjust the inputs, watch it respond instantly, and export the result. No install, no account.

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Confidence IntervalsLive

what 95% really means

Controls

Presets

Sample size n

A confidence interval is often misread. It does not mean the true value has a 95% chance of being in one interval — it means that if you repeated the experiment many times, about 95% of the intervals would contain the true mean. The red intervals here are the unlucky ones that miss it.

▶ Run in Python

Data Inspector

Confidence level95%

Observed coverage0%

Intervals shown50

Governing equation

\overset{x}{ˉ} \pm z \frac{σ}{n} = 50 \pm 1.96 \cdot \frac{10}{30}

Reading this result: About 0% of these 50 intervals captured the true mean — close to the 95% you asked for. Raising n from 30 tightens each interval (SE = σ/√n) but does not change that hit rate: the confidence level, not the sample size, sets how often you are right.

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About this simulation

The full Confidence Intervals tool models a sampling error with the same numerics engineers and scientists use — running entirely client-side. Change any parameter and the result updates in real time, so you can build intuition, check a design, or teach the concept without spreadsheets or installs.

More you can do with Confidence Intervals

Confidence Intervals for an A/B test Confidence Intervals for a survey sample Confidence Intervals for a poll margin Confidence Intervals for a quality-control chart Confidence Intervals for a clinical trial Confidence Intervals for a customer churn Confidence Intervals for a click-through rate Confidence Intervals for an exam-score curve

Other ways to simulate a sampling error

Optimize + UQ for a sampling error Hypothesis Test for a sampling error Linear Regression for a sampling error Central Limit Theorem for a sampling error Bayesian Inference for a sampling error Bootstrap for a sampling error

Frequently asked questions

How do I simulate a sampling error?: Open this page and use the live Confidence Intervals tool below — set your inputs and the simulation runs instantly in your browser using real numerics. No install, no account needed.
Is it free?: Yes. The simulation runs free in your browser. A one-time unlock or a Pro plan adds advanced parameters, saved presets, data import, and clean exports.
Can I use my own numbers?: Absolutely — every input is adjustable, and with data import you can drive a sampling error from your own measurements.