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

Answer:

Option C) Increase; wider

Step-by-step explanation:

When constructing a confidence interval,

Margin of error =

$\text{Critical Value}\times \displaystyle\frac{\text{Standard Deviation}}{\sqrt{\text{Sample Size}}} = \text{Critical Value}\times \frac{\sigma}{\sqrt{n}}$

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.