Question

question 15
all else equal, an increase in sample size will cause a(n)
increase decrease
in the width of the confidence interval.

Explanation:

The formula for the width of a confidence interval (for example, for a population mean when the population standard deviation \(\sigma\) is known) is \(w = 2z_{\alpha/2}\frac{\sigma}{\sqrt{n}}\), where \(z_{\alpha/2}\) is a constant based on the confidence level, \(\sigma\) is the population standard deviation (assumed constant here), and \(n\) is the sample size. As \(n\) (sample size) increases, the value of \(\frac{\sigma}{\sqrt{n}}\) decreases. Since the width \(w\) is directly proportional to \(\frac{\sigma}{\sqrt{n}}\), an increase in \(n\) will lead to a decrease in the width of the confidence interval.

Answer:

decrease