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From what I understand, using t-distribution instead of normal distribution is a good idea when sample size is small. As a matter of fact, the bigger the sample grows, the closer its going to be to the normal distribution.

My question is, when I implement some algorithm, would there be some reason(aside from computational efficiency) I wouldn't want to use t-distribution to handle samples of all sizes, including large samples?

for example:

I want to generate confidence interval using a sample size 5, 10, 20 and 100 for a population of 1000 individuals.

Should i use t-distribution regardless of sample size with $\nu = $ 4, 9, 19 and 99 for the computation of my confidence interval statistic $t_{\frac{1-\alpha}{2};\nu}$?

Thanks a lot!

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Basic statistics courses teach us to use a normal distribution instead of a $t$ distribution for estimates on samples with size larger than some threshold (usually $n \geqslant 30$). This rule of thumb is a product of the historical context in which it arose. When it couldn't be assumed that everyone had access to reasonably powerful computing machines, it made sense to use a normal distribution when you could get away with it because using the $t$ distribution was more cumbersome. As you've suggested, there is little reason not to use a $t$ distribution for large samples as, for practical purposes, it is shaped identically to the normal distribution for large $n$.

The only circumstance I know of in which I would explicitly recommend using a normal distribution over a $t$ distribution given a large sample size is if your data doesn't satisfy the assumptions necessary for a $t$ distribution but you have a large enough $n$ to assume approximate normality.

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