Three randomly selected households are surveyed. The numbers of people in the households are 1, 4, and 10. Assume that samples of size n=2 are randomly selected with replacement from the population of 1, 4, and 10. Construct a probability distribution table that describes the sampling distribution of the proportion of even numbers when samples of sizes n=2 are randomly selected. Does the mean of the sample proportions equal the proportion of even numbers in thepopulation? Do the sample proportions target the value of the populationproportion? Does the sample proportion make a good estimator of the populationproportion? Listed below are the nine possible samples.

1,11,41,104,14,44,1010,110,410,10

Construct the probability distribution table.

Sample Proportion

Probability

0.25

0

0.1

nothing

0.25

0.5

0.75

nothing

0.25

1

0.75

nothing

(Type the integer orfraction.)

Choose the correct answer below.

A.

The proportion of even numbers in the population is equal to the mean of the sample proportions.

B.

The proportion of even numbers in the population is equal to the mean of the sample proportions of odd numbers.

C.

The proportion of odd numbers in the population is equal to the mean of the sample proportions of even numbers.

D.

The proportion of even numbers in the population is not equal to the mean of the sample proportions.

Choose the correct answer below.

A.

The sample proportions do not target the proportion of even numbers in thepopulation, so sample proportions do not make good estimators of the population proportion.

B.

The sample proportions target the proportion of even numbers in thepopulation, so sample proportions do not make good estimators of the population proportion.

C.

The sample proportions do not target the proportion of even numbers in thepopulation, so sample proportions make good estimators of the population proportion.

D.

The sample proportions target the proportion of even numbers in thepopulation, so sample proportions make good estimators of the population proportion.