Express the confidence interval (47.1%, 58.1%) in the form of ☎± ME. % ± %
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
Express the confidence interval (47.1%,58.1%) in the form of P^±ME.
To express the given confidence interval in the form \(\hat{p} \pm ME\), follow these steps:
1. Calculate the point estimate \(\hat{p}\), which is the midpoint of the confidence interval:
\[
\hat{p} = \frac{47.1\% + 58.1\%}{2}
\]
2. Determine the margin of error (ME), which is the distance from the point estimate to either endpoint of the confidence interval:
\[
ME = 58.1\% - \hat{p} = \hat{p} - 47.1\%
\]
By solving these calculations, you will be able to express the given confidence interval in the required form.
Next, enter your calculations in the provided boxes:
- For the point estimate (\(\hat{p}\)): \(\phantom{X}\% \)
- For the margin of error (ME): \(\phantom{X}\% \)
Both values should reflect the understanding and correct application of confidence interval concepts.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4b94522a-bae3-4964-ba8a-526370d903b8%2F1b0a02e1-12a1-4ab2-94eb-c73694818467%2Fv20khi8_processed.png&w=3840&q=75)
Transcribed Image Text:### Confidence Interval Expression
Express the confidence interval (47.1%, 58.1%) in the form of \(\hat{p} \pm ME\).
To express the given confidence interval in the form \(\hat{p} \pm ME\), follow these steps:
1. Calculate the point estimate \(\hat{p}\), which is the midpoint of the confidence interval:
\[
\hat{p} = \frac{47.1\% + 58.1\%}{2}
\]
2. Determine the margin of error (ME), which is the distance from the point estimate to either endpoint of the confidence interval:
\[
ME = 58.1\% - \hat{p} = \hat{p} - 47.1\%
\]
By solving these calculations, you will be able to express the given confidence interval in the required form.
Next, enter your calculations in the provided boxes:
- For the point estimate (\(\hat{p}\)): \(\phantom{X}\% \)
- For the margin of error (ME): \(\phantom{X}\% \)
Both values should reflect the understanding and correct application of confidence interval concepts.
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