f size 2 is to be selected without replacement from this population. There are 12 possible samples (provided that the order in which observations are selected is taken into account). 3, 4 3, 5 3, 6 4, 3 4, 5 4, 6 5, 3 5, 4 5, 6 6, 3 6, 4 6, 5

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Consider the following population: {3, 4, 5, 6}. For this population the mean is

μ = 
3 + 4 + 5 + 6
4
 = 4.5

Suppose that a random sample of size 2 is to be selected without replacement from this population. There are 12 possible samples (provided that the order in which observations are selected is taken into account).

3, 4 3, 5 3, 6 4, 3 4, 5 4, 6
5, 3 5, 4 5, 6 6, 3 6, 4 6, 5
(a) Compute the sample mean for each of the 12 possible samples.
Sample Sample Mean
3, 4  
3, 5  
3, 6  
4, 3  
4, 5  
4, 6  
5, 3  
5, 4  
5, 6  
6, 3  
6, 4  
6, 5  

 

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