Instead of the large sample confidence interval formula for \(\mu\) on page 230, we could have given the alternative formula

\[\bar{x}-z_{\alpha / 3} \cdot \frac{\sigma}{\sqrt{n}}

Explain why the one on page 230 is narrower, and hence preferable, to the one given here.

EXAMPLE 6 Calculating and interpreting a large sample confidence interval A random sample of size n = 100 is taken from a population with = 5.1. Given that the sample mean is x = 21.6, construct a 95% confidence interval for the pop- ulation mean .