Mean and Variance Estimation: Importance of Normality for Confidence Intervals

[MaxManus]

Homework Statement

Why is it normality is much more important for making a confidence interval for the mean than for the variance?

You do use the estimated variance to make the mean confidence interval. So why is the mean confidence interval more robust against the normality assumtion?

$$\mu = \bar{x} +- t_{\alpha}\frac{S}{\sqrt{n}}$$

 

[lanedance]

not sure if i totally understand the question, but do you know the central limit theorem? have a think how that applies to the mean...