Homework SourseThe assets in billions of dollars of the four wealthiest peo
The assets (in billions of dollars) of the four wealthiest people in a particular country are 37, 34, 27, 19. Assume that samples of size n = 2 are randomly selected with replacement from this population of four values.
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.
Probability
Probability
37
28
35.5
27
34
26.5
32
23
30.5
19
Compare the mean of the population to the mean of the sampling distribution of the sample mean.
Do the sample means target the value of the population mean? In general, do sample means make good estimates of population means Why or Why not?
Please show steps to how you get the distinct means and it\'s corresponding probablities. I am confused to how to get the probabilities. Thanks in advance.
| Probability | Probability | ||
| 37 | 28 | ||
| 35.5 | 27 | ||
| 34 | 26.5 | ||
| 32 | 23 | ||
| 30.5 | 19 |
Solution
samples
mean
1
37,37
37
2
37,34
35.5
3
37,27
32
4
37,19
28
5
34,34
34
6
34,37
35.5
7
34,27
30.5
8
34,19
26.5
9
27,27
27
10
27,37
32
11
27,34
30.5
12
27,19
23
13
19,19
19
14
19,37
28
15
19,34
26.5
16
19,27
23
Frequency distributions of means are presented below.
Means
frequency
Probability
19
1
1/16=0.0625
23
2
2/16=0.125
26.5
2
2/16=0.125
27
1
1/16=0.0625
28
2
2/16=0.125
30.5
2
2/16=0.125
32
2
2/16=0.125
34
1
1/16=0.0625
35.5
2
2/16=0.125
37
1
1/16=0.0625
Total
16
1
Population mean = (37+34+27+19)/4 =29.25
Do the sample means target the value of the population mean?
The sample means do target the value of the population mean.
In general, do sample means make good estimates of population means Why or Why not?
In general, do sample means make good estimates of population means because sample mean is an unbiased estimator of population mean.
.
| samples | mean | |
| 1 | 37,37 | 37 |
| 2 | 37,34 | 35.5 |
| 3 | 37,27 | 32 |
| 4 | 37,19 | 28 |
| 5 | 34,34 | 34 |
| 6 | 34,37 | 35.5 |
| 7 | 34,27 | 30.5 |
| 8 | 34,19 | 26.5 |
| 9 | 27,27 | 27 |
| 10 | 27,37 | 32 |
| 11 | 27,34 | 30.5 |
| 12 | 27,19 | 23 |
| 13 | 19,19 | 19 |
| 14 | 19,37 | 28 |
| 15 | 19,34 | 26.5 |
| 16 | 19,27 | 23 |
