When to use a Z-test?

Use a Z-test when you know the population standard deviation (σ) and the sample size is large (n ≥ 30). If σ is unknown or n < 30, use a t-test instead.

The p-value is the probability of obtaining test results at least as extreme as the observed results, assuming the null hypothesis is true. p < 0.05 usually leads to rejecting the null hypothesis.

One-tailed vs Two-tailed?

Two-tailed tests for ANY difference (higher OR lower). One-tailed tests for a specific direction (e.g., is the mean HIGHER?). Two-tailed is the standard conservative approach.

Z-Test Calculator

Perform a one-sample Z-test to compare a sample mean to a population mean.

Sample Mean (x̄)

Population Mean (μ)

Hypothesized mean

Population SD (σ)

Sample Size (n)

Significance Level (α)

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Z-Statistic

0

p-value = 0

No Significant Difference

Since p >= 0.05, we fail to reject the null hypothesis. There is not enough evidence to say the means are different.

Sample Mean105

Population Mean100

Two-Tailed P-Value

Standard test

One-Tailed P-Value

Directional test

Documentation

Z-Test Formula

Z Statistic

Frequently Asked Questions

About the Z-Test

What it calculates

This z-test solves mathematical and statistical problems using standard formulas. Perform one-sample Z-test for known population SD.

When to use it

Use for homework, data analysis, exam prep, or quick verification of manual calculations.

Example

Adjust the inputs above to model your specific scenario with the Z-Test.

Explore More

Z-Test Calculator

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0

No Significant Difference

Z-Test Formula

About the Z-Test

Related Calculators

ANOVA (One-Way)

Chi-Square

p-value

Relative Risk

T-Test

Z-Score