**Question:** A population has a mean of 85.6 and a standard deviation of 9. Assume that a sampling distribution of sample means has been constructed, based on repeated samples of n = 225 from this population. What would be the value of the *standard error of the mean*? (Round your answer to the nearest tenth, if necessary). - ○ 0.6 - ○ 1.6667 - ○ 0.175 - ○ 0.1333 --- **Explanation:** To find the standard error of the mean (SEM), use the formula: \[ \text{SEM} = \frac{\sigma}{\sqrt{n}} \] where: - \(\sigma\) is the standard deviation of the population, - \(n\) is the sample size. In this scenario: - \(\sigma = 9\), - \(n = 225\). \[ \text{SEM} = \frac{9}{\sqrt{225}} = \frac{9}{15} = 0.6 \] Thus, the standard error of the mean is closest to **0.6**.
**Question:** A population has a mean of 85.6 and a standard deviation of 9. Assume that a sampling distribution of sample means has been constructed, based on repeated samples of n = 225 from this population. What would be the value of the *standard error of the mean*? (Round your answer to the nearest tenth, if necessary). - ○ 0.6 - ○ 1.6667 - ○ 0.175 - ○ 0.1333 --- **Explanation:** To find the standard error of the mean (SEM), use the formula: \[ \text{SEM} = \frac{\sigma}{\sqrt{n}} \] where: - \(\sigma\) is the standard deviation of the population, - \(n\) is the sample size. In this scenario: - \(\sigma = 9\), - \(n = 225\). \[ \text{SEM} = \frac{9}{\sqrt{225}} = \frac{9}{15} = 0.6 \] Thus, the standard error of the mean is closest to **0.6**.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
![**Question:**
A population has a mean of 85.6 and a standard deviation of 9. Assume that a sampling distribution of sample means has been constructed, based on repeated samples of n = 225 from this population.
What would be the value of the *standard error of the mean*? (Round your answer to the nearest tenth, if necessary).
- ○ 0.6
- ○ 1.6667
- ○ 0.175
- ○ 0.1333
---
**Explanation:**
To find the standard error of the mean (SEM), use the formula:
\[ \text{SEM} = \frac{\sigma}{\sqrt{n}} \]
where:
- \(\sigma\) is the standard deviation of the population,
- \(n\) is the sample size.
In this scenario:
- \(\sigma = 9\),
- \(n = 225\).
\[ \text{SEM} = \frac{9}{\sqrt{225}} = \frac{9}{15} = 0.6 \]
Thus, the standard error of the mean is closest to **0.6**.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fab974963-06b9-41af-b656-db2914f781bc%2Faf251920-4adb-491c-a7af-50d9b0f14a0c%2Fjyvtq1n.jpeg&w=3840&q=75)
Transcribed Image Text:**Question:**
A population has a mean of 85.6 and a standard deviation of 9. Assume that a sampling distribution of sample means has been constructed, based on repeated samples of n = 225 from this population.
What would be the value of the *standard error of the mean*? (Round your answer to the nearest tenth, if necessary).
- ○ 0.6
- ○ 1.6667
- ○ 0.175
- ○ 0.1333
---
**Explanation:**
To find the standard error of the mean (SEM), use the formula:
\[ \text{SEM} = \frac{\sigma}{\sqrt{n}} \]
where:
- \(\sigma\) is the standard deviation of the population,
- \(n\) is the sample size.
In this scenario:
- \(\sigma = 9\),
- \(n = 225\).
\[ \text{SEM} = \frac{9}{\sqrt{225}} = \frac{9}{15} = 0.6 \]
Thus, the standard error of the mean is closest to **0.6**.
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