Answer to Question #197770 in Statistics and Probability for Carl

Question #197770

Random samples of size n=2 are drawn from a finite population consisting of the numbers 5,67,8 and 9. Compute the mean, variance and standard deviation of the population, and the me a variance and standard deviation of the sample means. Showtablr with complete solutions


1
Expert's answer
2021-05-25T09:01:52-0400

We have given the population,

5,6,7,8and95,6,7,8 \hspace{2mm}and \hspace{2mm}9

Population mean = 5+6+7+8+95=7\dfrac{5+6+7+8+9}{5} = 7


Variance =(57)2+(67)2+(77)2+(87)2+(97)25= \dfrac{(5-7)^2+(6-7)^2+(7-7)^2+(8-7)^2+(9-7)^2}{5}\\


=4+1+0+1+45=2= \dfrac{4+1+0+1+4}{5} = 2


Standard Deviation =2=1.41= \sqrt{2} = 1.41

Table for sampling distribution can be formed as




Variance of sampling distribution =

(5.57)2+(67)2+2(6.57)2+2(77)2+2(7.57)2+(87)2+(8.57)210=2.25+1+0.5+0+0.5+1+2.2510=0.75\dfrac{(5.5-7)^2+(6-7)^2+2(6.5-7)^2+2(7-7)^2+2(7.5-7)^2+(8-7)^2+(8.5-7)^2}{10}\\ = \dfrac{2.25+1+0.5+0+0.5+1+2.25}{10} \\ = 0.75


Sample standard deviation =0.75=0.86= \sqrt{0.75} = 0.86


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