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 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 describe the sampling distribution of the proportion of even numbers when samples of sizes n = 2 are randomly selected. Does the mean of the sample proportion equal the proportion of even numbers in the population? Do the sample proportion 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 sample 3.3 3.4 3.11 4.5 4.4 4.11 11.3 11.4 11.11

Explanation / Answer

here as there are 3*3 =9 samples possible therefore probability of each sample is 1/9

let x1 and x2 are 2 sample values ; therefore distibution of their proportion of even values are given below:

adding duplicate values final table looks like this

please revert if there are subparts of it.

x1 x2 sample proportion probability 3 3 0    1/9 4 3 1/2 1/9 11 3 0    1/9 3 4 1/2 1/9 4 4 1    1/9 11 4 1/2 1/9 3 11 0    1/9 4 11 1/2 1/9 11 11 0    1/9

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