Question

In determining the sample size necessary to estimate a population proportion, which of the following is NOT needed?

a. the mean of the population
b. the maximum margin of error that can be tolerated
c. the confidence level required
d. a preliminary estimate of the true population proportion p

Answer 1

a. the mean of the population

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:

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

To find the sample size necessary we need values of M(maximum margin of error), z(related to the confidence level) and
`\pi`, which is an estimate of the true population proportion p.

The mean of the population is not needed.

So the correct answer is:

a. the mean of the population