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

Question

Three randomly selected households are surveyed The numbers of people in the households are 2, 7, and 12. Assume that samples of size n 2 are randomly selected with replacement from the population of 2, 7, and 12. 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 2,7 2.12 7.2 77 7,12 12,2 12,7 12, 12 Construct the probability distribution table. Sample Proportion Probability Type an integer or fraction Choose the correct answer below. O A. The proportion of odd numbers in the population is equal to the mean of the sample proportions of even numbers O B. The proportion of odd numbers in the population is not equal to the mean of the sample proportions. O C. The proportion of odd numbers in the population is equal to the mean of the sample proportions OD. The proportion of even numbers in the population is equal to the mean of the sample proportions of odd numbers.

Explanation / Answer

a) The proportion of odd numbers can be 0, 0.5 or 1. Hence,

The probability distribution table will be:

b) Option C is correct.

c) Option C is correct.

Sample Proportion Probability 0 4/9 0.5 4/9 1 1/9

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