Three randomly selected households are surveyed. The numbers of people in the ho

Question

Three randomly selected households are surveyed. The numbers of people in the households are 4, 5, and 9. Assume that samples of size n = 2 are randomly selected with replacement from the population of 4, 5, and 9. 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 number 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. Construct the probability distribution table.

Explanation / Answer

Sample proportion for both are even number when n = 2 is 2/2 = 1

Sample proportion for 1 is even number when n =1 is 1/2 = 0.5

Sample proportion for 0 is even number(both are odd) when n = 0 is 0/2 = 0

From the given data

Sample proportion Probability

1 1/9

0.5 4/9

0 4/9

Mean of the sample proporiton = 1*1/9 + 0.5*4/9 = 3/9 = 1/3 = 0.3333

Population proporiton P = 1/3 = 0.3333

Since sample proportion is good estimator to the population proportion

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