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 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. 4.4 4.5 4.9 5.4 5.5 5.9 9.4 9.5 9.9 Construct the probability distributor table. Choose the correct answer below. A. The proportion of odd numbers in the population is equal to the mean of the sample proportions of even numbers. B. The proportion of odd numbers in the population is not equal to the mean of the sample proportions. C. The proportion of odd numbers in the population is equal to the mean of the sample proportions. D. The proportion of even numbers in the population is equal to the mean of the sample proportions of odd numbers. Choose the correct answer below A. The sample proportions target the proportion of odd numbers in the population so sample proportions do not make good estimators of the population proportion. B. The sample proportions do not target the proportion of odd numbers in the population so sample proportions do not make good estimators of the population proportion. C. The sample proportions target the proportion of odd numbers in the population so sample proportions make good estimators of the population proportion. D. The sample proportions do not target the proportion of odd numbers in the population so sample proportions make good estimators of the population proportion.

Explanation / Answer

possible values for proportion of odd numbers are 0,0.5,1 i.e n no odd number, one of them is odd , both are odd numbers

=>

sample proportion ………probability

0…………………………….1/9

0.5…………………………4/9

1……………………………4/9

mean of sample = 0 * 1/9 + 0.5 * 4/9 + 1 * 4/9 = 0.67

hence

proportion of odd numbers in the population is equal to the mean of sample population

choose C)

the correct choice us C)

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