## Introductory Statistics 9th Edition

N=5000, n=300, $n/N$ = $300/5000$=0.06, which is less than .05. When σ=25, $\sigma_{\bar{x}\ }$ = $\frac{σ}{\sqrt n}$ = $\frac{25}{\sqrt 300}$ = 1.443 B. N=5000, n=100, $n/N$ = $100/5000$=0.02, which is less than .05. When σ=25, $\sigma_{\bar{x}\ }$= $\frac{σ}{\sqrt n}$ = $\frac{25}{\sqrt 100}$ = 2.5
σ_${\bar{x}\ }$ = $\frac{σ}{\sqrt n}$ is used because $n/N$ is less than .05, where N is the population size and n is the sample size.