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 43, 30, 26,19,43, 30, 26, 19. Assume that samples of size n=2 are randomly selected with replacement from this population of four values.

a. After identifying the 16 different possible samples and finding the mean of each sample, construct a table representing the sampling distribution of the sample mean. In the table, values of the sample mean that are the same have been combined.
_
x                    Probability
43
28
36.5
26
34.5
24.5
31
22.5
30
19

(Type integers or fractions.)

Explanation / Answer

Sampling could pick 40 and then 40. That's one possible sample. You could draw 40 and then 25. That's another sample. You could draw 25 and then 40. That's a third sample. Find all possible samples below with their means

43, 43   X=43.0    43, 30    X=36.5   43, 26    X=34.5     43, 19     X=31.0

30, 43   X=36.5    30, 30    X=30.0   30, 26    X=28.0     30, 19       X=24.5

26, 43   X=34.5    26, 30    X=28.0   26, 26     X=26.0    26, 19       X=22.5

19, 43   X=31.0    19, 30    X=24.5   19, 26     X=22.5    19, 19       X=19.0

All sample sizes are 2, therefore the means are found by dividing the sum of the 2 sampled assets divided by 2.

The probabilities are found by counting numer of times a particular mean occurs in the above table of means.

Find the sampliing distribution below.

x      Probability

43.0      1/16              
28.0       1/8
36.5       1/8
26.0      1/16
34.5      1/8
24.5       1/8
31.0       1/8
22.5       1/8
30.0      1/16
19.0      1/16

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