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 a Construct the probability distribution table. Sample Proportion Probability (Type an integer or fraction.)

Explanation / Answer

For different sampel taken, the proportion of odd numbers in the sample is computed as:

Using the above distribution as each of the sample is equally likely, therefore we get the distribution of the sample proportion as:

Sample 2,2 2,4 2,9 4,2 4,4 4,9 9,2 9,4 9,9 Sample proportion 0 0 0.5 0 0 0.5 0.5 0.5 1

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