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For Students · Hypothesis Test

Hypothesis Test for a p-value

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 p-value live below — adjust the inputs and watch it respond, right in your browser.

Hypothesis Test (z-test)Live

p-values & rejection regions

Controls

Presets

Sample mean x̄

Null mean μ₀

Std deviation s

Sample size n

Two-tailed test

A hypothesis test asks whether a sample mean is far enough from the null value to be surprising by chance alone. The test statistic z measures that distance in standard errors; if it falls in the red rejection region (p below 0.05) we reject the null. Larger samples shrink the standard error and sharpen the test.

▶ Run in Python

Data Inspector

Standard error1.265

z-statistic1.581

p-value0.1138

Decisionfail to reject

Governing equation

z = \frac{x ˉ - μ _{0}}{σ / n} = \frac{52 - 50}{8/ 40} = 1.58

Reading this result: The statistic sits in the white central zone, so the gap between x̄ and μ₀ is within ordinary sampling noise and you fail to reject H₀.

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Frequently asked questions

Is this good for students?: Yes — this version of "Hypothesis Test for a p-value" 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.