Question

The assets (in billions of dollars) of the four wealthiest people in a particular country are 38,27,19,18. 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.

Answer 1

To construct the sampling distribution of the sample mean, find the mean of each possible sample of size 2 and create a table to represent the sampling distribution.

Step-by-step explanation:

To construct the sampling distribution of the sample mean, we need to find the mean of each possible sample of size 2.

The possible samples and their means are:

Sample 1: 38, 38 → Mean: 38

Sample 2: 27, 27 → Mean: 27

Sample 3: 19, 19 → Mean: 19

Sample 4: 18, 18 → Mean: 18

Sample 5: 38, 27 → Mean: 32.5

Sample 6: 38, 19 → Mean: 28.5

Sample 7: 38, 18 → Mean: 28

Sample 8: 27, 38 → Mean: 32.5

Sample 9: 27, 19 → Mean: 23

Sample 10: 27, 18 → Mean: 22.5

Sample 11: 19, 38 → Mean: 28.5

Sample 12: 19, 27 → Mean: 23

Sample 13: 19, 18 → Mean: 18.5

Sample 14: 18, 38 → Mean: 28

Sample 15: 18, 27 → Mean: 22.5

Sample 16: 18, 19 → Mean: 18.5

Now we can construct a table representing the sampling distribution of the sample mean:

SampleMean138227319418532.5628.5728832.59231022.51128.512231318.514281522.51618.5