Random sample of size 4 are drawn from the finite population which con

angepepagiortzb

angepepagiortzb

Answered question

2021-12-07

Random sample of size 4 are drawn from the finite population which consists of the numbers 2,3,7,8,and 10.
a. What is the population mean, population variance and population standard deviation of the given data?
b. What is the sampling distribution of the sample means for a sample of size 2 which can be drawn without replacement from the given population?
c. What is the mean, variance and standard deviation of the sampling distribution?

Answer & Explanation

Alfonso Miller

Alfonso Miller

Beginner2021-12-08Added 20 answers

Step 1 
Let μ  and  σ denote the population mean and the population standard deviation. 
Let x  and  s denote the sample mean and sample standard deviation. 
Where, σ=1Nx(xμ)2  and  s=1n1x(xx)2
Step 2 
a. Now, substitute the given data values in the formula, μ=xN. Where, the population size, N=5
μ=xN 
=2+3+7+8+105 
=305 
=6 
Now, substitute N=5  and  μ=6 in the formula σ=1Nx(xμ)2 to determine the population standard deviation. 
σ=1Nx(xμ)2 
=15x(x6)2 
=(26)2+(36)2+(76)2+(86)2+(106)25 
=9.2 
3.033 
The variance of the population is the square of the standard deviation, therefore, 
σ2=9.2 
Step 3 
b. There would be 10 possible samples from the population of size, 5, ((52)=10)
SampleSample mean(xm)(xmx)22,32+32=2.5(2.56)2=12.252,74.52.252,8512,10603,7513,85.50.253,106.50.257,87.52.257,108.56.258,1099SUM6034.5 
Step 4 
The mean of the sampling distribution is given by x=xm10
x=xm10 
 

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