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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.

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Q: What is the difference between t test and z test?
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