Question

When constructing a confidence interval, as the confidence level required in estimating the mean increases, the width of the confidence interval _________.a. remains the sameb. increasesc. decreases

Answer 1

b. increases

Explanation:

The width of a confidence interval of x%, that is, the margin of error of the interval, is given by:

`M = z*(\sigma)/(√(n))`

In which z is dependent on the confidence interval, and related to the z table. A higher confidence level means a higher pvalue in the z table, so a higher value of z.

The width M and z are direct proportional. That is, as z increases, so does M.

So the correct answer is:

b. increases