### Sampling Distribution: An Educational Guide#### Understanding the Problem StatementLet's delve into a statistical problem involving the assets of the four wealthiest individuals in a country. The assets, in billions of dollars, are as follows:- 39- 28- 22- 13We are assuming that samples of size \( n = 2 \) are randomly selected with replacement from this set of four values.#### Constructing the Sampling DistributionTo create the sampling distribution of the sample mean, we must first identify all 16 possible samples and calculate the mean for each. These values are then grouped, and their corresponding probabilities are determined.#### The Table of Sample MeansBelow is the table constructed from the problem:| \( \bar{x} \) | Probability | | \( \bar{x} \) | Probability ||---------------|-------------|---|---------------|-------------|| 39 | | | 25 | || 33.5 | | | 22 | || 30.5 | | | 20.5 | || 28 | | | 17.5 | || 26 | | | 13 | |**Note:** Fill in the probabilities as integers or fractions as specified in the problem.#### ExplanationHere is a detailed explanation of what is expected in each step of the process:1. **Identify Possible Samples:** Each sample is of size 2 and is selected with replacement. This results in a total of \( 4 \times 4 = 16 \) possible samples since each of the four assets can pair with any other, including itself. 2. **Calculate the Mean:** For each sample, compute the sample mean (\( \bar{x} \)). For example, if the sample is (39, 22), the mean is \( \frac{39 + 22}{2} = 30.5 \).3. **Count Occurrences:** Determine how frequently each unique sample mean occurs among all possible samples.4. **Determine Probabilities:** The probability of each unique sample mean is derived by dividing its frequency by the total number of samples (16).This method provides a comprehensive approach to understanding how sample means distribute when drawn from a small, finite population. By working these steps, one gains

Name: ### Sampling Distribution: An Educational Guide#### Understanding the
Uploaded: 2024-03-20T07:06:41.000Z
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Description: ### Sampling Distribution: An Educational Guide#### Understanding the Problem StatementLet's delve into a statistical problem involving the assets of the four wealthiest individuals in a country. The assets, in billions of dollars, are as follows:-

Given information: The data represents the assets of the four wealthiest people in a particular…

Math

Statistics

The assets (in billions of dollars) of the four wealthiest people in a particular country are 39, 28, 22, 13. Assume that samples of sizen=2 are randomly selected with replacement from this population of four values.