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

Answer 1

The larger sample sizes gives a narrower confidence interval

Explanation:

The larger sample sizes gives a narrower confidence interval, that is, a more "precise" estimation of the elections results.

In a confidence interval of proportions, we have that the lower end is given by:

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

In which
`\pi` is the probability of a sucess,
`z` is a value from the Z table and n is the length of the sample.

The upper end is given by:

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

As n increases, the difference between U and L decreases. This means that the confidence interval gets narrower.