Confidence limits of the mean for large samples

In practice, however, we usually have one sample, of known mean, and we require a range for fi, the true value. Equation (2.6) can be rearranged to give this  

Equation (2.7) gives the 95% confidence interval of the mean. The 95% confidence limits are x 1.96ct/Vw. 

In practice we are unlikely to know a exactly. However, provided that the sample is large, a can be replaced by its estimate, s. 

Other confidence limits are sometimes used, in particular the 99% and 99.7% confidence limits. 

For large samples, the confidence limits of the mean are given by 

---