What conditions must be met to use a Z-test for a population mean?
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Population standard deviation (σ) is known
This is the key difference from the t-test (where σ is unknown).
Random sampling
The data should come from a random and representative sample.
Normality condition
The population should be normally distributed or
The sample size is large (n≥30), so the Central Limit Theorem makes the sampling distribution of the mean approximately normal.
to use a z-test for a population mean: the population standard deviation (σ) must be known, and either the population is normally distributed or the sample size is large (n ≥ 30).