Question

b. Given a population size of 4,3,2,4 and 2. Assume a sampling without replacement.

(a) find the population mean and standard deviation

(b) the sample mean and sample standard deviation.

Answer 1

(a) Given population is 4,3,2,4,2

Population mean $\mu=\dfrac{4+3+2+4+2}{5}=\dfrac{15}{5}=3$

Standard deviation $\sigma=\sqrt{\dfrac{\sum (x-\mu)^2}{n}}$

$=\sqrt{\dfrac{(1)^2+0^2+(-1)^2+(1)^2+(-1)^2}{5}}\\[9pt]=\sqrt{\dfrac{4}{5}}\\[9pt]=\sqrt{0.8}=0.894$

(b) sample mean $x=\mu=3$

Sample standard deviation $s=\dfrac{\sigma}{\sqrt{n}}$

$=\dfrac{0.894}{\sqrt{5}}\\[9pt]=\dfrac{0.894}{2.245}=0.39$