Question

What happens to the standard error each time you quadruple the sample size?

Answer 1

Quadrupling the sample size reduces the standard error by half.

Explanation:

The standard error is given by

`SE=sigma/sqrtn`

If we substitute `4n` for `n`, this becomes:

`SE=sigma/sqrt(4n)=sigma/(2sqrtn)=1/2sigma/sqrtn`

So the standard error has been reduced by half.