Question

Out of 3000 students in a School of Public Health, 1500 students defined themselves regular dietary supplement users. If you take a sample of 20 of them, what’s the standard error of the proportion (p) of those who defined themselves as dietary supplement users in the school? (Give your answer to at least 3 decimal places)

Answer 1

The standard error of the proportion is 0.112.

Explanation:

The standard error of a proportion is given by the following formula:

`S = \sqrt{(p(1-p))/(n)}`

In which p is the probability of a success and n is the length of the sample.

In this problem

A success is a student defining themselves regular dietary supplement users. Our of 3000 students, 1500 do. So
`p = (1500)/(3000) = 0.5`.

We take a sample of 20 of them, so
`n = 20`.

So

`S = \sqrt{(p(1-p))/(n)} = \sqrt{(0.5*0.5)/(20)} = 0.112`