Question 395264
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.