Question

I collect a random sample of size n from a population and compute a 95% confidence interval for the proportion I observe from the population. What could I do to produce a new confidence interval with a smaller width, smaller margin of error, based on these same data?

Answer 1

You should increase the size of your random sample, that is, increase the value of n.

Explanation:

In a sample with a number n of people surveyed with a probability of a success of
`\pi`, and a confidence interval
`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:

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

This means that as we increase the sample size(n), the margin of error decreases, as does the width of the confidence interval.

What could I do to produce a new confidence interval with a smaller width, smaller margin of error, based on these same data?

You should increase the size of your random sample, that is, increase the value of n.