SOLUTION: If you are performing a one sample hypothesis test of the mean and the standard deviation of the population is unknown, do you use a t-test or a z-test?

Question 395264: If you are performing a one sample hypothesis test of the mean and the standard deviation of the population is unknown, do you use a t-test or a z-test?
Answer by jrfrunner(365) (Show Source): You can put this solution on YOUR website!
the appropriate test "always" when the population variance is unknown is to use a t-test. although as the samples sizes get larger and larger, the t-test and Z-test will converge but this does not happen (based on my experience) until the sample size is greater than 100.
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The other wrinkle is that if the sample size is small, and the population variance is unknown, you can only use the t-test if the sample comes from a normal distribution as the central limit theorem can't help you with small samples.
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