Question
Three randomly selected households are surveyed. The numbers of people in the households are 2, 6, and 7. Assume that samples of size n = 2 are randomly selected with replacement from the population of 2, 6, and 7. 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. 2, 2 2, 6 2, 7 6, 2 6, 6 6, 7 7, 2 7, 6 7, 7 Construct the probability distribution table. Sample Proportion Probability Choose the correct answer below The proportion of even numbers in the population is equal to the mean of the sample proportions. The proportion of even numbers in the population is not equal to the mean of the sample proportions. The proportion of even numbers in the population is equal to the mean of the sample proportions of odd numbers. The proportion of odd numbers in the population is equal to the mean of the sample proportions of even numbers Choose the correct answer below The sample proportions do not target the proportion of even numbers in the population, so sample proportions do not make good estimators of the population proportion
Explanation / Answer
The proportion of even numbers can be 0, 0.5 and 1.
Hence,
The probability distribution will be:
For next part, Option A is correct.
For last part, choose the option having "Do target" and "do make good estimators".
Sample Proportion Probability 0 4/9 0.5 4/9 1 1/9
