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math.hypothesis-testing-z Calculator
Performs a one-sample z-test from sample mean, population parameters, and sample size, computing z-statistic and p-value. The z-test requires knowing the population standard deviation — when it's estimated from the sample, use the t-test instead.
Inputs
Sample Mean
Arithmetic average. Sensitive to outliers — if your data has extreme values, the median may be more representative.
Population Mean
Arithmetic average. Sensitive to outliers — if your data has extreme values, the median may be more representative.
Population Std
Reference formula or conversion factor shown for context.
Sample Size
Number of data points collected. Larger samples give narrower confidence intervals. Rule of thumb: 30+ for most statistical tests.
Results
z-statistic
The value at the specified point or condition.
p-value (two-tailed, approx)
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.