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A statistical hypothesis test using the normal distribution to compare means when variance is known or sample size is large.
DESCRIPTION
A z-test evaluates hypotheses about population means assuming known variance or large samples enabling normal approximation. It computes a standardized z-statistic that is compared against critical values to accept or reject the null hypothesis. Common applications include A/B tests on proportions (via normal approximation) and comparing a sample mean to a known benchmark. The z-test is closely related to the t-test, which is preferred when variance is unknown and sample size is small. Correct assumptions and proper tail selection are crucial for valid inference.
ALTERNATIVE DEFINITIONS
Wikipedia
In statistics, a z-test is a hypothesis test used when the test statistic follows a normal distribution.
States the core assumption about normality of the test statistic.
Stat Trek
A z-test is a statistical test used to determine whether two population means are different when the variances are known and the sample size is large.
Highlights known variances and large-sample requirement.
Penn State STAT 500
When σ is known and the sample size is large, the test statistic is approximately normal and a z-test may be used.
Educational framing of conditions for using a z-test.
RELATED TERMS
Hypothesis Testing Normal Distribution p-value Confidence Interval Central Limit Theorem Type I Error One-tailed Test Two-tailed Test Standard Deviation
COMPETING TERMS
KNOWLEDGE AREAS
Mathematics Data Science Testing & Validation
TARGET AUDIENCE
Data Scientist Data Analyst BI Specialist
EXTERNAL SOURCES
- Wikipedia - Z-test
- Penn State - Course notes on z-tests
- Khan Academy - Video on z-statistics
- IBM SPSS - Documentation on one-sample z-test
TOP QUESTIONS
When should the z-test be used over the t-test?
Use the z-test when population variance is known or sample size is large enough for normal approximation. Otherwise, prefer the t-test for small samples with unknown variance.
Category: Requirements
How is the z-statistic computed in a z-test?
Subtract the hypothesized mean from the sample mean and divide by the standard error, then compare to the standard normal distribution.
Category: HowTo
What assumptions does the z-test require?
Independent observations, known variance or large samples, and approximate normality of the sampling distribution under the null hypothesis.
Category: Requirements
What are common mistakes with z-tests?
Using a z-test for small samples with unknown variance, mis-specifying one-tailed vs two-tailed tests, and misunderstanding p-values versus effect sizes.
Category: Mistakes
What is the risk of misusing a z-test?
Incorrect conclusions due to violated assumptions or inflated Type I errors. This can misguide decisions in A/B testing and analytics.
Category: Risk
Is the z-test relevant in modern data science?
Yes, it remains foundational for proportion tests and large-sample scenarios. It complements resampling and Bayesian methods.
Category: Relevancy
What is currently a hot topic around the z-test?
Using z-tests with sequential analysis and controlling for multiple testing in large-scale experiments is actively discussed.
Category: Topic
How to interpret p-values in a z-test?
The p-value indicates the probability of observing data at least as extreme under the null. It is not the probability the null is true.
Category: Misunderstanding
Where should I learn more about the z-test?
Read university course notes, statistical textbooks, and online tutorials like Penn State STAT 500 and Khan Academy.
Category: Learning