The Z-Test › The Z-Test

Michael BrenndoerferUpdated January 12, 20262 min read
Machine Learning from ScratchAll chapters
Part 2 of 9Hypothesis Testing
Chapter 14The Z-Test › The Z-Test
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You've learned what p-values mean. You understand how to set up null and alternative hypotheses. You know what assumptions matter. Now it's time to put all of that knowledge into practice with your first complete hypothesis test.

The z-test is the natural starting point because it's the simplest parametric test. When you know the population standard deviation, the z-test gives you exact inference based on the familiar normal distribution. No approximations, no complex formulas, just a straightforward application of everything you've learned so far.

Knowing the population standard deviation is rare in practice, so why learn the z-test at all? Two reasons. First, it's the foundation for understanding more complex tests like the t-test (next chapter). Second, z-tests are the standard approach for testing proportions, which is one of the most common hypothesis testing scenarios in data science, from A/B testing to clinical trials to quality control.