Determine and o u=78, o=18, n = 36 from the given parameters of the
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Determine u and o from the given parameters of the population and sample size
U = 78
O = 18
N = 36
![**Instruction: Determining Sample Mean and Standard Deviation**
Given the parameters of the population, calculate the sample mean \((\mu_{\bar{x}})\) and sample standard deviation \((\sigma_{\bar{x}})\).
**Population Parameters:**
- Population Mean (\(\mu\)) = 78
- Population Standard Deviation (\(\sigma\)) = 18
- Sample Size (\(n\)) = 36
**Calculation:**
1. **Sample Mean (\(\mu_{\bar{x}}\))**
- Since the sample mean is the same as the population mean:
\[
\mu_{\bar{x}} = \mu = 78
\]
2. **Sample Standard Deviation (\(\sigma_{\bar{x}}\))**
- Calculated using the formula:
\[
\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}}
\]
- Substituting the given values:
\[
\sigma_{\bar{x}} = \frac{18}{\sqrt{36}} = \frac{18}{6} = 3
\]
**Conclusion:**
- Sample Mean \((\mu_{\bar{x}})\) = 78
- Sample Standard Deviation \((\sigma_{\bar{x}})\) = 3
**Visual Explanation:**
- There are no graphs or diagrams included in the given text. The information appears in a simple textual format with two empty boxes indicating spaces where these calculated values should be entered.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1506ec02-adda-4113-8c13-92d681b7a885%2F98da963a-bf47-4efd-a67c-7d7bd32da5f0%2Fyb17qqm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Instruction: Determining Sample Mean and Standard Deviation**
Given the parameters of the population, calculate the sample mean \((\mu_{\bar{x}})\) and sample standard deviation \((\sigma_{\bar{x}})\).
**Population Parameters:**
- Population Mean (\(\mu\)) = 78
- Population Standard Deviation (\(\sigma\)) = 18
- Sample Size (\(n\)) = 36
**Calculation:**
1. **Sample Mean (\(\mu_{\bar{x}}\))**
- Since the sample mean is the same as the population mean:
\[
\mu_{\bar{x}} = \mu = 78
\]
2. **Sample Standard Deviation (\(\sigma_{\bar{x}}\))**
- Calculated using the formula:
\[
\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}}
\]
- Substituting the given values:
\[
\sigma_{\bar{x}} = \frac{18}{\sqrt{36}} = \frac{18}{6} = 3
\]
**Conclusion:**
- Sample Mean \((\mu_{\bar{x}})\) = 78
- Sample Standard Deviation \((\sigma_{\bar{x}})\) = 3
**Visual Explanation:**
- There are no graphs or diagrams included in the given text. The information appears in a simple textual format with two empty boxes indicating spaces where these calculated values should be entered.
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