Determine and o; from the given parameters of the population and sample size. H= 55, o = 6, n= 40
Determine and o; from the given parameters of the population and sample size. H= 55, o = 6, n= 40
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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Question
![**Instructions:**
Determine \( \mu_{\bar{x}} \) and \( \sigma_{\bar{x}} \) from the given parameters of the population and sample size.
Given:
- \( \mu = 55 \)
- \( \sigma = 6 \)
- \( n = 40 \)
**Calculation:**
1. **Population Mean for Sample (\( \mu_{\bar{x}} \)):**
Since the sample mean is an unbiased estimator for the population mean, \( \mu_{\bar{x}} \) is equal to the population mean \( \mu \).
\[ \mu_{\bar{x}} = 55 \]
2. **Standard Deviation of the Sample Mean (\( \sigma_{\bar{x}} \)):**
Use the formula for the standard deviation of the sample mean:
\[ \sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}} \]
Calculate:
\[ \sigma_{\bar{x}} = \frac{6}{\sqrt{40}} \]
\[ \sigma_{\bar{x}} = \frac{6}{6.32} \approx 0.95 \]
**Answers:**
- \( \mu_{\bar{x}} = 55 \)
- \( \sigma_{\bar{x}} \approx 0.95 \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fac9c6941-fcbd-4d0f-a0fa-57d2e8e41463%2Fe647ba61-a648-472a-b90c-429bcb4290c5%2Fhg714qe_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Instructions:**
Determine \( \mu_{\bar{x}} \) and \( \sigma_{\bar{x}} \) from the given parameters of the population and sample size.
Given:
- \( \mu = 55 \)
- \( \sigma = 6 \)
- \( n = 40 \)
**Calculation:**
1. **Population Mean for Sample (\( \mu_{\bar{x}} \)):**
Since the sample mean is an unbiased estimator for the population mean, \( \mu_{\bar{x}} \) is equal to the population mean \( \mu \).
\[ \mu_{\bar{x}} = 55 \]
2. **Standard Deviation of the Sample Mean (\( \sigma_{\bar{x}} \)):**
Use the formula for the standard deviation of the sample mean:
\[ \sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}} \]
Calculate:
\[ \sigma_{\bar{x}} = \frac{6}{\sqrt{40}} \]
\[ \sigma_{\bar{x}} = \frac{6}{6.32} \approx 0.95 \]
**Answers:**
- \( \mu_{\bar{x}} = 55 \)
- \( \sigma_{\bar{x}} \approx 0.95 \)
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