The assets (in billions of dollars) of the four wealthiest people in a particula

Question

The assets (in billions of dollars) of the four wealthiest people in a particular country are 44, 34, 13, 11. Assume that samples of size 2 are randomly selected with replacement from this population of four values. After listing the possible samples and finding the mean of each sample, use a table to describe the sampling distribution of the sample means. Find the mean of the sampling distribution. The mean of the sample means is. (Round to two decimal places as needed.) Is the mean of the sampling distribution [from part (b)] equal to the mean of the population of the four listed values? If so, are those means always equal? No, the mean of the sample means is not equal to the mean of the population. These means are not always equal, because the mean is a biased estimator. Yes, the mean of the sample means is equal to the mean of the population. These means are always equal, because the mean is a biased estimator. No, the mean of the sample means is not equal to the mean of the population. These means are not always equal, because the mean is an unbiased estimator. Yes, the mean of the sample means is equal to the mean of the population. These means are always equal, because the mean is an unbiased estimator.

Explanation / Answer

Consider the possible samples:

a)

Hence,

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b)

Consider:

Thus,  
  
E(x) = Expected value = mean = Sum(xP(x)) =    25.5 [ANSWER]

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C)

As we can see, the mean of 44, 34, 13, 11 is 25.5.

Hence, it is an unbiased estimator,

OPTION D. [ANSWER]

44 44 44 34 44 13 44 11 34 44 34 34 34 13 34 11 13 44 13 34 13 13 13 11 11 44 11 34 11 13 11 11

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