Question

A simple random sample of size 36 is drawn from finite population consisting of 101 units. If the population S.D. is 12.6, find the standard error of sample means when the sample is drawn

a) with replacement

b) without replacement

Answer 1

a) with replacement

$$\sigma_{\bar{X}}=\dfrac{\sigma}{\sqrt{n}}=\dfrac{12.6}{\sqrt{36}}=2.1$$

b) without replacement

$$\sigma_{\bar{X}}=\dfrac{\sigma}{\sqrt{n}}\sqrt{\dfrac{N-n}{N-1}}=\dfrac{12.6}{\sqrt{36}}\sqrt{\dfrac{101-36}{101-1}}$$

$$=0.21\sqrt{65}\approx1.693$$