I understand entirely that unbiased estimators of population variance are not normally distributed. And so they have their own distribution, namely the t-distribution. So far so good. Now, by the CLT, shouldn't the t-distribution approach normality? So, for a sufficiently large sample size (and consequently 'degrees of freedom') we shouldn't have to consider t at all. If I am right in my thinking so far, how large a sample needs to be taken in order to think that the sample variances will be Normally distributed and the t-distribution becomes irrelevant? My current text book is not clear. I want to be able to say something along the lines of "Well, the sample size is >50, so let's just use the normal distribution" Thank you if you have ploughed through that, and thank you again if you can put me right.