Question

In the months leading up to an election, news organizations conduct many surveys to help predict the results of the election. Often news organizations will increase the sample size in the last few weeks before the election. Which of the following is the primary reason they increase the sample size?

A. A larger sample size gives a narrower confidence interval.
B. A larger sample size allows more people to give their input.
C. A larger sample size gives a higher confidence level.
D. A larger sample size means the sampling method isn’t as important.

Answer 1

A. A larger sample size gives a narrower confidence interval.

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 margin of error is given by:

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

As the sample size increases(n increases), the margin of error decreases, given a narrower, more precise confidence interval.

So the correct answer is:

A. A larger sample size gives a narrower confidence interval.