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For Students · Survey Analysis

Survey Analysis for a sampling error

Built for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition. Simulate a sampling error live below — adjust the inputs and watch it respond, right in your browser.

Confidence Interval

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Confidence IntervalsLive

what 95% really means

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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.

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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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Distributions

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Probability DistributionsLive

PDF / PMF explorer

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Mean μ

Std dev σ

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Data Inspector

Distributionnormal

Mean0.000

Variance1.000

Std dev1.000

Governing equation

f (x) = \frac{1}{2 π 1.00} e^{- \frac{( x - 0 ) ^{2}}{2 \cdot 1.00}}

Reading this result: The mean μ only slides the bell sideways while σ sets its width — variance is σ² = 1.00, so doubling σ quadruples the spread.

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Frequently asked questions

Is this good for students?: Yes — this version of "Survey Analysis for a sampling error" is framed for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.