Use the given confidence interval to find the margin of error and the sample mean. (13.5,20.7) The sample mean is. (Type an integer or a decimal.)
Use the given confidence interval to find the margin of error and the sample mean. (13.5,20.7) The sample mean is. (Type an integer or a decimal.)
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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![**Finding the Margin of Error and Sample Mean from a Confidence Interval**
To solve this, we use the given confidence interval \( (13.5, 20.7) \).
**Definitions**:
- **Confidence Interval**: A range of values used to estimate the true value of a population parameter.
- **Sample Mean (\(\bar{x}\))**: The average value of a sample.
- **Margin of Error (E)**: Reflects the amount of random sampling error in a survey's results.
**Steps to Find the Sample Mean and Margin of Error**:
1. **Sample Mean Calculation**:
\[
\text{Sample Mean} (\bar{x}) = \frac{\text{Lower Limit} + \text{Upper Limit}}{2}
\]
\[
\bar{x} = \frac{13.5 + 20.7}{2} = 17.1
\]
2. **Margin of Error Calculation**:
\[
E = \frac{\text{Upper Limit} - \text{Lower Limit}}{2}
\]
\[
E = \frac{20.7 - 13.5}{2} = 3.6
\]
**Conclusion**:
- The sample mean is 17.1.
- The margin of error is 3.6.
This exercise provides a basic understanding of how to extract key statistical values from a confidence interval, essential in survey analysis and interpretation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F026bd461-1467-4394-8d30-2d6a7a09468a%2F401a5d0a-3951-4b76-86d4-967f4479cb05%2Fmqotpcc.jpeg&w=3840&q=75)
Transcribed Image Text:**Finding the Margin of Error and Sample Mean from a Confidence Interval**
To solve this, we use the given confidence interval \( (13.5, 20.7) \).
**Definitions**:
- **Confidence Interval**: A range of values used to estimate the true value of a population parameter.
- **Sample Mean (\(\bar{x}\))**: The average value of a sample.
- **Margin of Error (E)**: Reflects the amount of random sampling error in a survey's results.
**Steps to Find the Sample Mean and Margin of Error**:
1. **Sample Mean Calculation**:
\[
\text{Sample Mean} (\bar{x}) = \frac{\text{Lower Limit} + \text{Upper Limit}}{2}
\]
\[
\bar{x} = \frac{13.5 + 20.7}{2} = 17.1
\]
2. **Margin of Error Calculation**:
\[
E = \frac{\text{Upper Limit} - \text{Lower Limit}}{2}
\]
\[
E = \frac{20.7 - 13.5}{2} = 3.6
\]
**Conclusion**:
- The sample mean is 17.1.
- The margin of error is 3.6.
This exercise provides a basic understanding of how to extract key statistical values from a confidence interval, essential in survey analysis and interpretation.
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