Question

Consider two x distributions corresponding to the same x distribution. The first x distribution is based on samples of size n = 100 and the second is based on samples of size n = 225. Which x distribution has the smaller standard error?

Answer 1

Hence the correct option is the distribution with n = 225 will have a smaller standard error.

Explanation:

Now the standard deviation is

`S.E=(\sigma )/(√(n))`

If n = 100 then consider
`\sigma =6`

`S.E=(6)/(√(100))=0.6`.

If n= 225 then consider
`\sigma =6`

`S.E=(6)/(√(225))=0.4`.

Here the distribution with n = 225 will have a smaller standard error.