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) The margin of error becomes smaller
C) Amount of sampling error increases
D) The margin of error increases

Answer 1

B) The margin of error becomes smaller

Explanation:

In a sample with a number n of people surveyed with a probability of a success of
`\pi`, and a confidence level of
`1-\alpha`, we have the following confidence interval of proportions.

`\pi \pm z\sqrt{(\pi(1-\pi))/(n)}`

In which

z is the zscore that has a pvalue of
`1 - (\alpha)/(2)`.

The width of the confidence interval is given by:

`W = z\sqrt{(\pi(1-\pi))/(n)}`

So as n increases, the width, or margin of error, becomes smaller.

As your sample size increases (let us say from 100 to 400 cases), which of the following becomes true?

The answer is:

B) The margin of error becomes smaller