Question

Imagine that you are conducting a poll to determine the percentage of adults who gamble at least once a month. As your sample size increases (let us say from 100 to 400 cases), which of the following becomes true?

A. Confidence interval becomes wider
B. Margin of error becomes smaller
C. Amount of sampling error increases
D. Margin of error increases

Answer 1

Option B) Margin of error becomes smaller

Explanation:

We are given the following information in the question:

A poll to determine the percentage of adults who gamble at least once a month.

We have to find what happens to the confidence interval as the sample size increases.

Margin of error =

`\text{Critical Value}* \displaystyle(\sigma)/(√(n))`

Confidence interval:

`\mu \pm \text{Margin of error}`

As the sample size increases, the margin of error decreases.

As the margin of error decreases the width of the confidence interval decreases.

Option B) Margin of error becomes smaller