SOLUTION: A population consists of the values (1, 4, 3, 2). Consider samples of size 2 that can be drawn from this population. a. List down all the possible samples and correspondin

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Question 1187884: A population consists of the values (1, 4, 3, 2). Consider samples of size 2 that can be drawn from this population.

a. List down all the possible samples and corresponding sample mean.

b. Construct the sampling distribution of the sample means.

c. Draw a histogram of the sampling distribution of the means.
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
We sample with replacement, so it's possible to choose the same value twice.
Here are the 16 possible samples of size 2:

sample     x̄     
(1,1)     1.0
(1,2)     1.5
(1,3)     2.0
(1,4)     2.5
(2,1)     1.5
(2,2)     2.0
(2,3)     2.5
(2,4)     3.0
(3,1)     2.0
(3,2)     2.5
(3,3)     3.0
(3,4)     3.5
(4,1)     2.5
(4,2)     3.0
(4,3)     3.5
(4,4)     4.0

There are 7 possible sample means. We list each sample with its frequency,
which is the number of times it occurs in the list of 16 above:

   x̄     f   
  1.0    1    
  1.5    2    
  2.0    3    
  2.5    4    
  3.0    3    
  3.5    2    
  4.0    1    

Here's the histogram:




Edwin