Question

fill in the blanks. the margin of error ____ with an increased sample size and ____ with an increase in confidence level. a. increases; decreases b. decreases; decreases c. decreases, increases d. increases; increases

Explanation:

The formula for the margin of error \(E = z\times\frac{\sigma}{\sqrt{n}}\) (for population mean when population standard deviation \(\sigma\) is known). As the sample size \(n\) increases, since \(n\) is in the denominator, \(\frac{\sigma}{\sqrt{n}}\) decreases, so \(E\) decreases. As the confidence level increases, the critical value \(z\) (which is related to the confidence level) increases. For example, for a 90% confidence level \(z = 1.645\), for a 95% confidence level \(z=1.96\), for a 99% confidence level \(z = 2.576\). Since \(z\) is in the numerator, when \(z\) increases, \(E\) increases.

Answer:

C. decreases, increases