Question

1. all else equal, an increase in sample size will cause a(n) increase/decrease (circle one) in the width of the confidence interval.

Explanation:

Step1: <Formula for confidence interval width>

The width of a confidence interval for a population mean (when population standard deviation \(\sigma\) is known) is \(2\times z_{\alpha/2}\times\frac{\sigma}{\sqrt{n}}\), where \(z_{\alpha/2}\) is the critical value, \(\sigma\) is the population standard deviation and \(n\) is the sample size.

Step2: <Effect of \(n\) on width>

As \(n\) increases, the value of \(\frac{\sigma}{\sqrt{n}}\) decreases. Since the width is proportional to \(\frac{\sigma}{\sqrt{n}}\) (because \(z_{\alpha/2}\) and \(\sigma\) are constant when "all else equal"), the width of the confidence interval decreases.

Answer:

decrease