Use this calculator to perform a one-sample z-test, comparing a sample mean to a known population mean when the population standard deviation is known. Enter the sample mean, population mean, population standard deviation, and sample size to get the z-statistic and approximate two-tailed p-value. This tool is for educational and preliminary analysis only.
One Sample Z-Test Calculator
Enter the sample mean, hypothesized population mean, known population standard deviation, and sample size.
* Note: This test is used when the population standard deviation is known.
Step 1: Enter Data
Enter the sample mean.
Enter the hypothesized mean.
Standard deviation of the population.
Enter the sample size.
Select the alternative hypothesis.
How It Works
The z‑statistic is computed as: $$ z = \frac{\bar{x} – \mu_0}{\sigma/\sqrt{n}}. $$
Depending on the alternative hypothesis, the p‑value is computed as follows:
– Two‑sided: \( p = 2\left[1-\Phi\left(|z|\right)\right] \)
– Right‑tailed: \( p = 1-\Phi(z) \)
– Left‑tailed: \( p = \Phi(z) \)