Three randomly selected households arc surveyed The numbers of people in the hou

Question

Three randomly selected households arc surveyed The numbers of people in the households are 2, 4, and 9. Assume that samples of sure 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 Construct the probability distribution table (Type an integer or fraction.)

Explanation / Answer

Construct the probability distribution table

Let X be the number of odd numbers, There is one observation with 2 odd numbers, 4 observations of 0 and 1 odd numbers.

X P(X) 0 4/9 = 0.444 1 4/9 = 0.444 2 1/9 = 0.111

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