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 2, 4, and 9. Assume that samples of size n = 2 are randomly selected with replacement from the population of 2, 4, and 9. 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. 2,2 2,4 2,9 4,2 4,4 4,9 9,2 9,4 9,9

Explanation / Answer

THE POSSIBLE OUTCOMES = (2,2)(2,4)(2,9)(4,2)(4,4)(4,9)(9,2)(9,4)(9,9)

NOW WE NEED TO FIND THE SAMPLE PROPORTION AND THE PROBABILITY OF EACH 2,4,9

FREQUENCY TABLE

X F(X) SAMPLE PROPORTION PROBABILITY

2 6 33.33% 0.3333

4 6 33.33% 0.3333

9 6 33.33% 0.3333

NOW THE PROPORTION OF EVEN AND ODD NUMBER

FOR EVEN BOTH 2 AND 4 WILL BE COUNTED

THEREFORE PROPOTION = 66.66% THEREFORE PROBABILITY = 0.6666

FOR ODD NUMBER ONLY 9 WILL BE COUNTED

THEREFORE PROPORTION = 33.33%

THEREFOREE PROBABILITY = 0.3333

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