Consider the population consisting of the values (1, 3, 8).
a. List all the possible samples of size 2 with replacement.
b. Compute the mean of each sample.
c. Identify the probability of each sample.
d. Compute the mean of the sampling distribution of the means.
e. Compute the population mean.
f. Compare the population mean with the mean of the sampling distribution of means.
Answers
Given : population consisting of the values (1, 3, 8).
To Find : List all the possible samples of size 2 with replacement.
Solution:
population (1, 3, 8).
all the possible samples of size 2 with replacement.
{ ( 1 , 1) , ( 1 , 3) , ( 1 , 8) , ( 3 , 1) , ( 3 , 3) , (3 , 8) , ( 8 , 1) , ( 8 , 3) , ( 8 , 8) }
mean of each sample.
(1 + 1)/2 = 1
(1 + 3)/2 = 2
(1 + 8)/2 = 4.5
(3 + 1)/2 = 3
(3 + 3)/2 = 3
(3 + 8)/2 = 5.5
(8 + 1)/2 = 4.5
(8 + 3)/2 = 5.5
(8 + 8)/2 = 8
( 1 , 3) and ( 3, 1) are same sample with probability = 2/9
( 1, 8) and ( 8 , 1) are same sample with probability = 2/9
( 3, 8) and ( 8 , 3) are same sample with probability = 2/9
( 1, 1) , (3 , 3) and ( 8, 8) are each with probability = 1/9
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