when should you use a Z-test instead of a T-test?
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- Known Population Standard Deviation: A Z-test is appropriate when the population standard deviation (σ\sigmaσ) is known. If the population standard deviation is unknown, a T-test should be used instead.
- Large Sample Size: If the sample size is large (typically n>30n > 30n>30), the Central Limit Theorem ensures that the sampling distribution of the sample mean will be approximately normal, allowing the use of a Z-test. Even when the population standard deviation is unknown, a large sample size can allow the Z-test to be appropriate due to the normal approximation.
- Normal Distribution or Large Sample Size: When the sample size is small (less than 30), the data should follow a normal distribution to use a Z-test. However, for small sample sizes and unknown population standard deviation, a T-test is preferred, as the T-distribution accounts for more variability.