The term Z-test is often used to refer specifically to the one-sample location test comparing the mean of a set of measurements to a given constant.
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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.
Whereas a t-test is used for n30, where n=sample size. n < 30 or n > 30 is not entirely arbitrary; it is intended to indicate that n must be sufficiently large to use the normal distribution. In some cases, n must be greater than 50. Note, both the t-test and the z-test can only be used if the distribution from which the sample is being drawn is a normal distribution. A z-test can be used even if the distribution is not normal (but is not severely skewed) if n>30, in which case, we can safely assume that the distribution is normal.
The answer depends on what is being tested: the t-test, F-test, Chi-square, Z-test are all commonly used with the Normal distribution. There are many others.
It depends on the population.Use t-test for a small population, N < 30; otherwiase, apply z-test or when N>=30.
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