Three randomly selected households are surveyed. The numbers of people in the households are 1​, 2​, and 12. Assume that samples of size n=2 are randomly selected with replacement from the population of 1​,

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Three randomly selected households are surveyed. The numbers of people in the households are
1​,
2​,
and
12.
Assume that samples of size
n=2
are randomly selected with replacement from the population of
1​,
2​,
and
12.
Construct a probability distribution table that describes the sampling distribution of the proportion of
odd
numbers when samples of sizes
n=2
are randomly selected. Does the mean of the sample proportions equal the proportion of
odd
numbers in the​population? Do the sample proportions target the value of the population​ proportion? Does the sample proportion make a good estimator of the population​ proportion? Listed below are the nine possible samples.
 
1​,1   
1​,2   
1​,12   
2​,1   
2​,2   
2​,12   
12​,1   
12​,2   
12​,12
 
Construct the probability distribution table.
 
Sample Proportion
Probability
 
0.1
0.25
0
nothing
 
0.5
0.25
0.75
nothing
 
0.75
0.25
1
nothing
​(Type an integer or​ fraction.)
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