Chapter 9, Problem 68CR

The interval from –2.33 to 1.75 captures an area of 0.95 under the z curve. This implies that another large-sample 95% confidence interval for μ has lower limit $\bar{x}-2.33\frac{\sigma }{\sqrt{n}}$ and upper limit $\bar{x}+1.75\frac{\sigma }{\sqrt{n}}.$ Would you recommend using this 95% interval over the 95% interval $x\pm 1.96\frac{\sigma }{\sqrt{n}}$ discussed in the text? Explain. (Hint: Look at the width of each interval.)