Question #186114

Consider a population consisting of the values (1, 3, 8), n= 2 with replacement.


  1. mean of sampling distribution of means
  2. variance of the sampling distribution of means
  3. standard deviation of the sampling distribution
1
Expert's answer
2021-05-07T09:33:13-0400

Solution:

Possible sample of size 2 with replacement={(1,3)(3,8)(1,8),(1,1),(3,3),(8,8)}=\{(1,3)(3,8)(1,8),(1,1),(3,3),(8,8)\}

Sample means for these samples={2,5.5,4.5,1,3,8}=\{2,5.5,4.5,1,3,8\}

(1): Mean of sample means=(2+5.5+4.5+1+3+8)/6=4=(2+5.5+4.5+1+3+8)/6=4

Population mean=(1+3+8)/3=4=(1+3+8)/3=4

Population variance,σ2=(14)2+(34)2+(84)23=263,\sigma^2=\dfrac{(1-4)^2+(3-4)^2+(8-4)^2}{3}=\dfrac{26}3

(2): The variance of the sampling distribution of means,σx2=σ2(Nn)n(N1),\sigma_x^2=\dfrac{\sigma^2(N-n)}{n(N-1)}

=263(32)2(31)=136=\dfrac{\dfrac{26}3(3-2)}{2(3-1)}=\dfrac{13}6

(3): The standard deviation of the sampling distribution,σx=136,\sigma_x=\sqrt{\dfrac{13}6}


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