Table of Contents
What Is a Z-Test?
A z-test is a statistical hypothesis test that uses the standard normal distribution to determine whether sample data provides sufficient evidence to reject a null hypothesis about a population parameter. The z-test is appropriate when the population standard deviation is known or when the sample size is large (n > 30), by the Central Limit Theorem.
The one-sample z-test compares a sample mean to a hypothesized population mean, while the two-sample z-test compares the means of two independent groups. The z-test produces a z-statistic that is compared to critical values from the standard normal distribution to determine statistical significance.
Formula
Critical Z-Values
| Significance (α) | One-Tailed | Two-Tailed |
|---|---|---|
| 0.10 | 1.282 | 1.645 |
| 0.05 | 1.645 | 1.960 |
| 0.01 | 2.326 | 2.576 |
| 0.001 | 3.090 | 3.291 |
Frequently Asked Questions
When should I use a z-test instead of a t-test?
Use a z-test when the population standard deviation is known (rare in practice) or when the sample size is large (n > 30) and you can use the sample standard deviation as a good estimate. In practice, the t-test is more commonly used because the population standard deviation is almost never known with certainty.
What does a significant z-test result mean?
A significant result (p-value < alpha) means the sample data is unlikely to have occurred if the null hypothesis were true. It provides evidence to reject the null hypothesis. However, statistical significance does not imply practical significance. Always examine the effect size and confidence interval to assess the practical importance of the finding.