Question

For a population of size N=120 with a mean of 7.5 and a standard deviation of 1.5, find the estimated standard error of the mean for the following sample sizes:(i)n=9 (ii)n=25 ?

Answer 1

Standard Error for Sample - 1 `sigma_barx=0.483`
Standard Error for Sample - 2 `sigma_barx=0.2679`

Explanation:

Given -

Population size `N=120`
Standard Deviation `sigma=1.5`
Sample Mean `barx=7.5`
Sample-1 size `n_1=9`
Sample-2 size`n_2=25`

Standard Error `sigma_barx=?`

Standard Error for Sample - 2

`sigma_barx=sigma/(sqrtn). sqrt((N-n_1)/(N-1))=1.5/sqrt25 xx sqrt((120-25)/(120-1))=1.5/5 xxsqrt(95/119)=0.3xx0.893=0.2679`