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I want to confirm something, i have to compare two means(using test statistics) and if i am not wrong and what i learnt is right then i must use T-test when sample size is less than 30 and population standard deviation is unknown(estimating the population SD with sample SD) otherwise Z-test. But if sample size is greater than 30 but SD is unknown, should i use T-test? I think i should use T-test because if sample size is greater than 30 , still it is not large enough to estimate the SD exactly. Will someone please confirm this ?

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  • $\begingroup$ I think you will find that if you do a $t$-test and a $z$-test on the same dataset with a large $n$ the results are more or less indistinguishable. $\endgroup$ – mdewey Dec 3 '16 at 13:24
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In addition to gRRRR's answer, which is right (use t-test for unknown standard deviation of population and z-test for known SD, the later being an unusual situation), please notice that when sample size is large (n larger than 100 or 1000) t-Student distribution converges to normal, and therefore z-test and t-test yield nearly the same result. For that reason, it's often said that you can use the simpler z-test for large samples even if SD is unknown.

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You are right, you should use the t-test whenever the population SD is unknown. The requirement of known population variance is what makes the use of z-test so limited.

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