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The"t" test, (called the "small 't' test, to distinguish it from the large 'T' test) is a test for deviation from a known norm, using a smaller sample set than the one required by the large T test. It is said to have been developed by the head of quality control at the Guinness Brewery in Ireland.
t test, because the z test requires knowing the population standard deviation and that's rare. The t test embodies an estimate of the standard deviation.
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It depends on the population.Use t-test for a small population, N < 30; otherwiase, apply z-test or when N>=30.