Question

In: Statistics and Probability

The assets​ (in billions of​ dollars) of the four wealthiest people in a particular country are...

The assets​ (in billions of​ dollars) of the four wealthiest people in a particular country are 33, 30, 19, 12.

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.

Xbar

Probability

Xbar

Probability

33

22.5

31.5

21

30

19

26

15.5

24.5

12

Solutions

Expert Solution

a)

below is sampling distribution of sample mean :

x1 x2 probabilityP(x1,x2)
33 33    1/16 33
33 30    1/16 31.5
33 19    1/16 26
33 12    1/16 22.5
30 33    1/16 31.5
30 30    1/16 30
30 19    1/16 24.5
30 12    1/16 21
19 33    1/16 26
19 30    1/16 24.5
19 19    1/16 19
19 12    1/16 15.5
12 33    1/16 22.5
12 30    1/16 21
12 19    1/16 15.5
12 12    1/16 12
sample sample
mean probability mean probability
33    1/16 22.5    1/8
31.5    1/8 21    1/8
30    1/16 19    1/16
26    1/8 15.5    1/8
24.5    1/8 12    1/16

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