Computing a mean confidence interval without storing all the data points

Question

For large n (see below for how to determine what\'s large enough), it\'s safe to treat, by the central limit theorem, the distribution of the sample mean as nor

Answer 1

I think that you don't have to worry so much about the size of n because it will soon exceed the number of 30, where the distribution can be considered as normal. Using Bayesian recursion to make posterior inference on the population mean and variance parameters, assuming a normal model, is I think the best way, if you don't want to store any data points from previous samples. You can take a look at this document for joint inference for the mean and variance, and specifically equations 38a, 38b and 38c.