Question

If the population standard deviation is σ = 8, how large a sample is necessary to have a standard error that is less than or equal to the following number of points? (Answer as a whole number.)

(a) 4 points

n =

(b) 2 points

n =

(c) 1 point

n =

Answer 1

We know the following

$\\\text{Standard Error}=\frac{\sigma}{\sqrt{n}}\\ n = {(\frac{\sigma}{\text{Standard Error}})}^2$

Given
$\sigma = 8$

a.
SE = 4
$n = {(\frac{8}{4})}^2 = 4$

b.
SE = 2
$n = {(\frac{8}{2})}^2 = 16$

c.
SE = 1
$n = {(\frac{8}{1})}^2 =64$