Student t-Distribution has been developed in order to estimate mean given small sample sizes. In contrast the Normal Distribution is applied when we know sample is taken from a normally distributed population and we know the population standard deviation .

Question

Assuming we selected a larger sample size [n>1000], how would the confidence interval using Student t-Distribution versus using Normal Distribution relate to each other?

The question is, when we use large sample sizes to estimate a population mean would it still matter if we use Student t-Distribution or Normal Distribution? Would the confidence intervals still be different or would they become the same, when using the two methods of distribution?

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