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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
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.
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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