21.4% 4.5 % 0/
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
![Title: Understanding Confidence Intervals in Trilnear Inequalities
---
**Expression of Confidence Interval**
In statistical analysis, a confidence interval provides a range of values that is likely to contain a population parameter. The given task is to express the confidence interval in the form of a trilinear inequality.
**Problem Statement:**
Express the confidence interval \(21.4\% \pm 4.5\%\) in the form of a trilinear inequality.
**Instructions:**
- Calculate the lower bound of the confidence interval by subtracting the margin of error from the given percentage.
- Calculate the upper bound by adding the margin of error to the given percentage.
- Format the result as a trilinear inequality.
---
**Calculation:**
1. **Given values:**
- Confidence Interval: \(21.4\%\)
- Margin of Error: \(\pm 4.5\%\)
2. **Lower Bound Calculation:**
\[
21.4\% - 4.5\% = 16.9\%
\]
3. **Upper Bound Calculation:**
\[
21.4\% + 4.5\% = 25.9\%
\]
4. **Trilinear Inequality Format:**
\[
16.9\% < p < 25.9\%
\]
**Conclusion:**
The confidence interval \(21.4\% \pm 4.5\%\) can be expressively and effectively stated as the trilinear inequality \(16.9\% < p < 25.9\%\). This represents the range within which the true population parameter \(p\) is expected to lie with a certain level of confidence.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6a01157b-f13c-43bf-adb3-4f12e47a4127%2F09d3608b-0a60-4027-9a9a-dbb2e2769961%2Fgrzb5uh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Title: Understanding Confidence Intervals in Trilnear Inequalities
---
**Expression of Confidence Interval**
In statistical analysis, a confidence interval provides a range of values that is likely to contain a population parameter. The given task is to express the confidence interval in the form of a trilinear inequality.
**Problem Statement:**
Express the confidence interval \(21.4\% \pm 4.5\%\) in the form of a trilinear inequality.
**Instructions:**
- Calculate the lower bound of the confidence interval by subtracting the margin of error from the given percentage.
- Calculate the upper bound by adding the margin of error to the given percentage.
- Format the result as a trilinear inequality.
---
**Calculation:**
1. **Given values:**
- Confidence Interval: \(21.4\%\)
- Margin of Error: \(\pm 4.5\%\)
2. **Lower Bound Calculation:**
\[
21.4\% - 4.5\% = 16.9\%
\]
3. **Upper Bound Calculation:**
\[
21.4\% + 4.5\% = 25.9\%
\]
4. **Trilinear Inequality Format:**
\[
16.9\% < p < 25.9\%
\]
**Conclusion:**
The confidence interval \(21.4\% \pm 4.5\%\) can be expressively and effectively stated as the trilinear inequality \(16.9\% < p < 25.9\%\). This represents the range within which the true population parameter \(p\) is expected to lie with a certain level of confidence.
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