Question

Complete the statement by filling in the blanks: When constructing a confidence interval, if the level of confidence increases, the margin of error must _____ and the confidence interval will be _____. Select one:

a. Decrease; wider
b. Decrease; narrower
c. Increase; wider
d. Increase; narrower

Answer 1

Option C) Increase; wider

Explanation:

When constructing a confidence interval,

Margin of error =

`\text{Critical Value}* \displaystyle\frac{\text{Standard Deviation}}{\sqrt{\text{Sample Size}}} = \text{Critical Value}* (\sigma)/(√(n))`

As the confidence level increases, the value for critical value increases and hence, the margin of error increases.

Confidence interval =

`\text{Sample mean} \pm \text{Margin of error}`

As the margin of error increases, the confidence interval will be wider.