Question

10 multiple choice 4 points select the most appropriate response. what will happen (other things being equal) if you decrease the confidence level for a given confidence interval? it will be narrower it will be wider it will not change

Explanation:

The width of a confidence interval is related to the confidence level. A lower confidence level means less certainty is required. This leads to a smaller critical value (e.g., for a normal distribution, \(z\)-score or \(t\)-score). Since the margin of error (which determines the width of the interval) is calculated as \(E = z\times\frac{\sigma}{\sqrt{n}}\) (for a z - interval, similar logic for t - interval), a smaller critical value (\(z\) or \(t\)) results in a smaller margin of error. A smaller margin of error makes the confidence interval narrower.

Answer:

It will be narrower