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math.stats-hypothesis-test Calculator
Performs one-sample hypothesis testing (z-test or t-test) from sample statistics and a null hypothesis, returning the test statistic and decision. A p-value below 0.05 rejects the null hypothesis at the 5% significance level — the standard threshold in most sciences.
Inputs
Xbar
Arithmetic average. Sensitive to outliers — if your data has extreme values, the median may be more representative.
Mu0
Arithmetic average. Sensitive to outliers — if your data has extreme values, the median may be more representative.
S
Reference formula or conversion factor shown for context.
N
Number of data points collected. Larger samples give narrower confidence intervals. Rule of thumb: 30+ for most statistical tests.
Results
t-statistic
The test statistic for a t-test. Compare to critical t for your chosen significance level (typically 1.96 for p < 0.05 with large samples).
degrees of freedom
The magnitude or severity on the applicable scale.
approx p-value
Probability of observing this result (or more extreme) if the null hypothesis were true. Below 0.05: conventionally significant. Below 0.01: strong evidence. A low p-value does not measure the size or practical importance of the effect.
result
The final computed result based on the given inputs.