Express the confidence interval 71.9 % ± 4.7 % in the form of a trilinear inequality. %
Express the confidence interval 71.9 % ± 4.7 % in the form of a trilinear inequality. %
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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![### Educational Website Transcription:
**Task:**
Express the confidence interval 71.9% ± 4.7% in the form of a trilinear inequality.
**Instructions:**
Fill in the blanks to express the confidence interval as an inequality:
\[ \_\_ \%\ <\ p\ <\ \_\_ \%\]
**Question Help:**
- [Message instructor](#)
**Submit:**
- Click "Submit Question" when completed.
**Explanation:**
A confidence interval provides a range of values within which a parameter, such as a population proportion, is expected to fall. To express this in a trilinear inequality:
1. Subtract the margin of error (4.7%) from the point estimate (71.9%) for the lower bound.
2. Add the margin of error (4.7%) to the point estimate (71.9%) for the upper bound.
\[ (71.9\% - 4.7\%)\ <\ p\ <\ (71.9\% + 4.7\%)\]
Calculate the bounds:
- Lower Bound: 67.2%
- Upper Bound: 76.6%
Thus, the trilinear inequality is:
\[ 67.2\% \ <\ p\ <\ 76.6\% \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8c0255f0-f478-421c-a420-8f7475329d1c%2F50eb5c30-8130-47b8-8e61-740a93a14a56%2F88bygwq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Educational Website Transcription:
**Task:**
Express the confidence interval 71.9% ± 4.7% in the form of a trilinear inequality.
**Instructions:**
Fill in the blanks to express the confidence interval as an inequality:
\[ \_\_ \%\ <\ p\ <\ \_\_ \%\]
**Question Help:**
- [Message instructor](#)
**Submit:**
- Click "Submit Question" when completed.
**Explanation:**
A confidence interval provides a range of values within which a parameter, such as a population proportion, is expected to fall. To express this in a trilinear inequality:
1. Subtract the margin of error (4.7%) from the point estimate (71.9%) for the lower bound.
2. Add the margin of error (4.7%) to the point estimate (71.9%) for the upper bound.
\[ (71.9\% - 4.7\%)\ <\ p\ <\ (71.9\% + 4.7\%)\]
Calculate the bounds:
- Lower Bound: 67.2%
- Upper Bound: 76.6%
Thus, the trilinear inequality is:
\[ 67.2\% \ <\ p\ <\ 76.6\% \]
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