PPolySim OS

Hypothesis Test (z-test)

Is that difference real or just luck? A hypothesis test measures how surprising your sample is under the null, and the p-value puts a number on it.

Hypothesis Test (z-test)Live

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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.

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Data Inspector

Standard error1.265
z-statistic1.581
p-value0.1138
Decisionfail to reject

Governing equation

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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How it works

A one-sample z-test compares a sample mean to a hypothesized value, measuring the gap in standard errors. If the test statistic lands in the rejection region — a p-value below the significance level — the null hypothesis is rejected. Larger samples shrink the standard error and make smaller effects detectable.

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Frequently asked questions

Is this hypothesis test p-value calculator tool really free?
Yes. Hypothesis Test (z-test) runs entirely in your browser using your device's own compute, so local use is free forever. You only pay Compute Tokens if you scale a job to the cloud.
Do I need to install anything?
No. Everything runs client-side in a modern browser — no downloads, no license, no account required to start.
Can I save or share my simulation?
Create a free account to save projects, and use a shareable embed or minted DOI to publish a live, interactive version anywhere.
How accurate are the results?
The solver uses established numerical methods, but results are for research and educational purposes and should be validated against experiment or professional review before you rely on them.