Question 1194763: Answer the following:
Five cities with the most Taiwanes-owned business in the Canada are given in the following table:
CITY NUMBER OF CHINESE-OWNED BUSINESS IN THOUSAND
Fancheska 42
Drafidol 39
Yusie 36
Teyuu 33
Retu 30
A.List all samples of size 4 and find the mean of each sample.
B. Consruct the sampling distribution of the sample mean.
Answer by ElectricPavlov(122)   (Show Source):
You can put this solution on YOUR website! **A. List all samples of size 4 and find the mean of each sample:**
1. **List all possible combinations of 4 cities:**
* F, D, Y, T
* F, D, Y, R
* F, D, T, R
* F, Y, T, R
* D, Y, T, R
2. **Calculate the mean of each sample:**
* F, D, Y, T: (42 + 39 + 36 + 33) / 4 = 37.5
* F, D, Y, R: (42 + 39 + 36 + 30) / 4 = 36.75
* F, D, T, R: (42 + 39 + 33 + 30) / 4 = 36
* F, Y, T, R: (42 + 36 + 33 + 30) / 4 = 35.25
* D, Y, T, R: (39 + 36 + 33 + 30) / 4 = 34.5
**B. Construct the sampling distribution of the sample mean**
The sampling distribution of the sample mean is a table or a graph that shows the probability of each possible sample mean occurring.
| Sample Mean | Frequency |
|---|---|
| 37.5 | 1 |
| 36.75 | 1 |
| 36 | 1 |
| 35.25 | 1 |
| 34.5 | 1 |
**Note:**
* Since we are sampling without replacement from a small population, the probabilities associated with each sample mean are not all equal.
* To calculate the exact probabilities, we would need to consider the combinations and permutations of selecting the cities.
This exercise demonstrates the concept of sampling distribution. By taking multiple samples and calculating their means, we can observe how the sample means vary around the population mean. In larger populations, the sampling distribution of the mean tends to approach a normal distribution, which is a key concept in statistical inference.
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