*Please explain. I\'ve been working on it for a while. I\'ve got a TI83 if that

Question

*Please explain. I've been working on it for a while. I've got a TI83 if that helps...

Three randomly selected households are surveyed. The numbers of people in the households are 3, 4, and 11. Assume that samples of size n = 2 are randomly selected with replacement from the population of 3, 4, and 11. Construct a probability distribution table that describes the sampling distribution of the proportion of even numbers when samples of sizes n = 2 are randomly selected. Does the mean of the sample proportions equal the proportion of even 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. 3, 3 3, 4 3, 11 4, 3 4, 4 4, 11 11, 3 11, 4 11, 11

Explanation / Answer

In 3, 4 and 11, there is only 1 even number. So, the sample proportion can be 0, 0.5 and 1.

P(0 even numbers) = 4/9

P(1 even number) = 4/9

P(2 even numbers) = 1/9

Hence,

The probability distribution table will be:

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

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