Student
Hi,
Is it correct to infer that we use t-distribution as an approximation of the sample distribution that is normally distributed (central limit theorem) based on the samples we have.
So the samples are an approximation of the population, and the t-distribution an approximation of the distribution of means of the samples, and we base our statistical inference on this t-distribution (like finding the confidence intervals, p-values, etc).
Teacher
Hello,
No, the t-distribution is always in a Gaussian model and it is an exact model. You don't use "approximate t distribution", it is just that we obtain a t distribution when we re-normalize the sample mean by the empirical standard deviation.
Best regards,
Timothée Mathieu