Standard Error is of Population Total

Question

We have the following data and we are required to obtain the standard error of unbiased estimate of the population total:

$N=160,n=64,\sigma^2=4$

My approach

We know that:

$SE(\bar{X})=\frac{\sigma}{\sqrt{n}}$ So, it can be written as:

$SE(\frac{Total}{n})=\frac{\sigma}{\sqrt{n}}$

Which in turn will be equal to:

$SE(Total)=(\sigma)(\sqrt{n})$.

In the above formula, after plugging in values, I am getting $SE=(2)(8)=16$

But this is not correct. The correct answer is $40$. Am I doing it incorrectly? I am not sure.

Any help?

Answer 1

The correct answer is obtained by multiplying the standard error with the total population.

S.E.$~=\frac{2}{8}\times160 =40$