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
p-values & rejection regions
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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.
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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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.
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No. Everything runs client-side in a modern browser — no downloads, no license, no account required to start.
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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.