The assets (in billions of dollars) of the four wealthiest people in a particular country are 32, 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. Probability X 32 31.5 31 27 26.5 (Type integers or fractions.) x 22 21.5 21 16.5 11 Probability

MATLAB: An Introduction with Applications
6th Edition
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Author:Amos Gilat
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Chapter1: Starting With Matlab
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The image displays a mathematical problem regarding sampling and probability. Here is the transcription and explanation:

---

**Problem Statement:**

The assets (in billions of dollars) of the four wealthiest people in a particular country are 32, 31, 22, and 11. Assume that samples of size n = 2 are randomly selected with replacement from this population of four values.

**Task:**

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.

**Table:**

| \(\bar{x}\) | Probability |
|-------------|-------------|
| 32          |             |
| 31.5        |             |
| 31          |             |
| 27          |             |
| 26.5        |             |
| 22          |             |
| 21.5        |             |
| 21          |             |
| 16.5        |             |
| 11          |             |

*(Type integers or fractions.)*

---

**Explanation:**

- The task involves calculating the sample means from all possible pairs of the provided asset values.
- After calculating the means, you are to fill in the corresponding probabilities in the table for each distinct sample mean.
- The probabilities will reflect how often each mean occurs relative to the total number of samples, which is 16 in this case.

This exercise is intended to teach about sampling distributions and how to identify the probability of specific sample means when samples are drawn with replacement.
Transcribed Image Text:The image displays a mathematical problem regarding sampling and probability. Here is the transcription and explanation: --- **Problem Statement:** The assets (in billions of dollars) of the four wealthiest people in a particular country are 32, 31, 22, and 11. Assume that samples of size n = 2 are randomly selected with replacement from this population of four values. **Task:** 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. **Table:** | \(\bar{x}\) | Probability | |-------------|-------------| | 32 | | | 31.5 | | | 31 | | | 27 | | | 26.5 | | | 22 | | | 21.5 | | | 21 | | | 16.5 | | | 11 | | *(Type integers or fractions.)* --- **Explanation:** - The task involves calculating the sample means from all possible pairs of the provided asset values. - After calculating the means, you are to fill in the corresponding probabilities in the table for each distinct sample mean. - The probabilities will reflect how often each mean occurs relative to the total number of samples, which is 16 in this case. This exercise is intended to teach about sampling distributions and how to identify the probability of specific sample means when samples are drawn with replacement.
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