Z Tests
One Sample Z Test Calculator
One Sample Z Test Calculator test a sample mean against a null mean when the population standard deviation is known.
Z Tests
One Sample Z Test Calculator
Test a sample mean against a null mean when the population standard deviation is known.
Formula
One-sample z test for a mean with known population sigma: z = (sample mean - null mean) / (population sigma / sqrt(n)); the p-value uses the selected normal tail.
About the One Sample Z Test Calculator
Test a sample mean against a null mean when the population standard deviation is known. Z procedures compare a standardized estimate with a normal reference distribution when their known-variance or large-sample conditions are satisfied.
How the One Sample Z Test Calculator Works
One-sample z test for a mean with known population sigma: z = (sample mean - null mean) / (population sigma / sqrt(n)); the p-value uses the selected normal tail.
The calculation runs in your browser. Submitted values are validated for the required numeric range, data shape, units, and method-specific restrictions before a result is shown.
Required Inputs
- Sample mean (required)
- Null mean (required)
- Known population standard deviation (required)
- Sample size (required)
- Alpha (required)
- Alternative hypothesis (required) Options: Two-tailed, Mean is greater, Mean is less
Results Reported
The result panel shows the final answer together with the intermediate quantities needed to audit the calculation. Depending on this method, reported values include:
sample_meannull_meanpopulation_sdsample_sizestandard_errorz_statisticp_valuedecision
One Sample Z Test Calculator Example
Paste the sample data, click Calculate, and compare the detailed table with the expected output.
| Input | Example value |
|---|---|
| Sample mean | 105 |
| Null mean | 100 |
| Known population standard deviation | 15 |
| Sample size | 36 |
| Alpha | 0.05 |
| Alternative hypothesis | two |
How to Use the Calculator
- Confirm that the calculator title and method match the quantity, test, conversion, or planning question you need to solve.
- Enter values with compatible units and the requested sample, group, matrix, count, date, or option format.
- Select Example Data to inspect a valid input layout, or enter your own values and select Calculate.
- Review the result table, formula, worked substitutions, warnings, and interpretation rather than using only the headline number.
- Use Copy Result or Download CSV when you need a reusable record of the displayed calculation.
Understanding the Result
Confirm independence, the correct null value, suitable expected counts for proportions, and whether population standard deviations are genuinely known for mean tests.
Keep the entered values, units, selected options, and any warning shown beside the result. For a hypothesis test, report the statistic, degrees of freedom where applicable, p-value, alpha level, effect size, and decision. For an estimate or conversion, report the formula convention and final unit.
Accuracy and Limitations
The calculator keeps full browser precision during calculation and rounds only for display. Accuracy still depends on correct inputs and on whether the displayed model represents the real problem. Educational calculators cannot replace required professional review, current official rules, field measurements, laboratory methods, or specialist statistical software where those are necessary.
Frequently Asked Questions
What does the One Sample Z Test Calculator calculate?
Test a sample mean against a null mean when the population standard deviation is known.
Which formula does the One Sample Z Test Calculator use?
One-sample z test for a mean with known population sigma: z = (sample mean - null mean) / (population sigma / sqrt(n)); the p-value uses the selected normal tail.
Is this calculator free to use?
Yes. Visitors can use it publicly through the shortcode page.
Does the calculator store visitor data?
No. Calculations run in the browser and do not store visitor data.