Homework Help is Here – Start Your Trial Now!
Math
Statistics
Express the confidence interval (13.8 %, 20 %) in the form of p + E.

Express the confidence interval (13.8 %, 20 %) in the form of p + E.

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
See similar textbooks
icon
Related questions
Question
### Expressing Confidence Intervals To express the confidence interval (13.8%, 20%) in the form of \( \hat{p} \pm E \), follow the steps below: 1. **Calculate \( \hat{p} \)**: - \( \hat{p} \) is the midpoint of the confidence interval. - Formula: \( \hat{p} = \frac{\text{Lower limit} + \text{Upper limit}}{2} \) - Calculation: \( \hat{p} = \frac{13.8\% + 20\%}{2} = 16.9\% \) 2. **Calculate \( E \)**: - \( E \) is the margin of error. - Formula: \( E = \text{Upper limit} - \hat{p} \) or \( E = \hat{p} - \text{Lower limit} \) - Calculation: \( E = 20\% - 16.9\% = 3.1\% \) 3. **Express the interval in the form of \( \hat{p} \pm E \)**: - Result: \( 16.9\% \pm 3.1\% \) Below this explanation, there are two boxes to fill in the calculated values: **Boxes Explanation:** - The first box is for \( \hat{p} \), which should be filled with **16.9%**. - The second box is for \( E \), which should be filled with **3.1%**. ### Visual Explanation - **Input Boxes:** - The left box: "16.9%" - The right box: "3.1%" This helps in visualizing and properly expressing confidence intervals in a precise mathematical format.
Transcribed Image Text:### Expressing Confidence Intervals To express the confidence interval (13.8%, 20%) in the form of \( \hat{p} \pm E \), follow the steps below: 1. **Calculate \( \hat{p} \)**: - \( \hat{p} \) is the midpoint of the confidence interval. - Formula: \( \hat{p} = \frac{\text{Lower limit} + \text{Upper limit}}{2} \) - Calculation: \( \hat{p} = \frac{13.8\% + 20\%}{2} = 16.9\% \) 2. **Calculate \( E \)**: - \( E \) is the margin of error. - Formula: \( E = \text{Upper limit} - \hat{p} \) or \( E = \hat{p} - \text{Lower limit} \) - Calculation: \( E = 20\% - 16.9\% = 3.1\% \) 3. **Express the interval in the form of \( \hat{p} \pm E \)**: - Result: \( 16.9\% \pm 3.1\% \) Below this explanation, there are two boxes to fill in the calculated values: **Boxes Explanation:** - The first box is for \( \hat{p} \), which should be filled with **16.9%**. - The second box is for \( E \), which should be filled with **3.1%**. ### Visual Explanation - **Input Boxes:** - The left box: "16.9%" - The right box: "3.1%" This helps in visualizing and properly expressing confidence intervals in a precise mathematical format.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman
SEE MORE TEXTBOOKS