One-sample z test
One-sample z test: use sample mean, null mean, known population standard deviation. Review the formula, worked example and calculation steps.
Inputs
Use the units shown—
Enter your values and select Calculate.
Formula & explanation
z = (sample mean − null mean) / (σ/√n)
Variables & units
- Sample mean
- Numeric value · minimum -1000000000000, maximum 1000000000000
- Null mean
- Numeric value · minimum -1000000000000, maximum 1000000000000
- Known population standard deviation
- Numeric value · minimum 0.000001, maximum 1000000000000
- Sample size
- Numeric value · minimum 1, maximum 1000000
Worked example
Mean105, null100, σ10, n25 gives z=2.5.
Assumptions
Assumes a known population SD and a justified normal sampling model.
Formula version 1.0.0. JavaScript floating-point arithmetic applies. Results display up to 6 decimal places; stored values retain available precision. Use the units shown.
Practice with an example
Use the default input values to find the answer. The reset icon restores those values.
Calculated on your device. Your latest 100 calculations stay in this browser.