If Z-statistics, when population variance is unknown, is a close approssimation of the T-statistics, which is better suited for the case, why do we overcomplicate things by using Z if sample size is over 30 and T if sample size is under 30 and not simply always use T?
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Welcome to Cross Validated! Who told you to do it this way? – Dave Apr 21 '22 at 00:11
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2I am not sure I accept the premises of the question. Who is we? If I believe that the assumptions for a t-statistic having a t-distribution are reasonably suitable, I use a t. If I use a normal approximation in similar circumstances it's because I am applying two asymptotic results (like CLT + Slutsky) that would suggest a large sample normal approximation would be suitable (typically not anything near $n\approx 30$ for the sorts of data I tend to be working with); typically if a normal approximation works for that, a t would be okay as well. Many posts on site have advice on these issues. – Glen_b Apr 21 '22 at 01:20
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Check the linked thread. It is simply not true that with >30 we use z-test. There is also nothing magical about sample size of >30 as discussed in https://stats.stackexchange.com/questions/2541/what-references-should-be-cited-to-support-using-30-as-a-large-enough-sample-siz and https://stats.stackexchange.com/questions/493349/can-we-always-assume-normal-distribution-if-n-30 Also, we always use z-test for binary data, regardless of sample size. – Tim Apr 21 '22 at 08:55