MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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![**Expressing Confidence Intervals**
When working with confidence intervals, it is often required to express the interval in a specific mathematical form. Consider the confidence interval (0.052, 0.120). We need to express it in the form \(\hat{p} - E < p < \hat{p} + E\).
To do this, follow these steps:
1. Calculate the midpoint, \(\hat{p}\), of the confidence interval. This is done by finding the average of the lower bound and the upper bound of the interval.
2. Determine the margin of error, \(E\), which is the difference between the midpoint and either bound of the interval.
For the given interval (0.052, 0.120):
- \(\hat{p} = \frac{0.052 + 0.120}{2}\)
- \(E = \frac{0.120 - 0.052}{2}\)
Now, express \(p\) in the form:
\[ \boxed{\hat{p} - E} < p < \boxed{\hat{p} + E} \]
On the website, you can enter the calculated values in the provided boxes:
\[ \boxed{ \_ \(\hat{p} - E\) \_ } < p < \boxed{ \_ \(\hat{p} + E\) \_ } \]
*Note: Type integers or decimals as required.*
By understanding these steps, students can easily work with confidence intervals and apply the necessary mathematical concepts to express them in the desired format.](https://content.bartleby.com/qna-images/question/8e2c67c3-55ad-4a91-97db-08b4cce36966/47f14117-0307-4954-b2f9-acbfbbf0288b/04pgb2_processed.jpeg)
Transcribed Image Text:**Expressing Confidence Intervals**
When working with confidence intervals, it is often required to express the interval in a specific mathematical form. Consider the confidence interval (0.052, 0.120). We need to express it in the form \(\hat{p} - E < p < \hat{p} + E\).
To do this, follow these steps:
1. Calculate the midpoint, \(\hat{p}\), of the confidence interval. This is done by finding the average of the lower bound and the upper bound of the interval.
2. Determine the margin of error, \(E\), which is the difference between the midpoint and either bound of the interval.
For the given interval (0.052, 0.120):
- \(\hat{p} = \frac{0.052 + 0.120}{2}\)
- \(E = \frac{0.120 - 0.052}{2}\)
Now, express \(p\) in the form:
\[ \boxed{\hat{p} - E} < p < \boxed{\hat{p} + E} \]
On the website, you can enter the calculated values in the provided boxes:
\[ \boxed{ \_ \(\hat{p} - E\) \_ } < p < \boxed{ \_ \(\hat{p} + E\) \_ } \]
*Note: Type integers or decimals as required.*
By understanding these steps, students can easily work with confidence intervals and apply the necessary mathematical concepts to express them in the desired format.
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