Q.10 - The Practice of Statistics for AP

Question

It's about ME Explain how each of the following would affect the margin of error of a confidence interval, if all other things remained the same.

(a) Increasing the confidence level

(b) Quadrupling the sample size

Step-by-Step Solution

Answer

(a) It increases the margin of error.

(b) It would reduce the margin of error.

Part (a) Step 1: Given Information

We have to explain how Increasing the confidence level would affect the margin of error of a confidence interval, if all other things remained the same. 

Part (a) Step 2: Explanation

The margin of error is directly related to the margin of error. The increase in the confidence level leads an increase in margin of error and vice versa. So, the increase in the confidence level would lead increase in the margin of error.

Part (b) Step 1: Given Information

We have to explain how Quadrupling the sample size  would affect the margin of error of a confidence interval, if all other things remained the same. 

Part (b) Step 2: Explanation

The margin of error is  inversely related to the margin of error. The increase in the size of the sample leads the reduction in margin of error and vice versa. So, the increase in the sample size would lead reduction in the margin of error.