A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x, is found to be 17.7, and the sample standard deviation, s, is found to be 4.3. (a) Construct a 96% confidence interval about µ if the sample size, n, is 39. (b) Construct a 96% confidence interval about u if the sample size, n, is 55. How does increasing the sample size affect the margin of error, E? (c) Construct a 98% confidence interval about u if the sample size, n, is 39. How does increasing the level of confidence affect the size of the margin of error, E? (d) If the sample sizo is 10 whot cond
A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x, is found to be 17.7, and the sample standard deviation, s, is found to be 4.3. (a) Construct a 96% confidence interval about µ if the sample size, n, is 39. (b) Construct a 96% confidence interval about u if the sample size, n, is 55. How does increasing the sample size affect the margin of error, E? (c) Construct a 98% confidence interval about u if the sample size, n, is 39. How does increasing the level of confidence affect the size of the margin of error, E? (d) If the sample sizo is 10 whot cond
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:**
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**Topic: Constructing Confidence Intervals**
A simple random sample of size \( n \) is drawn from a population that is normally distributed. The sample mean, \( \overline{x} \), is found to be 17.7, and the sample standard deviation, \( s \), is found to be 4.3.
(a) Construct a 96% confidence interval about \( \mu \) if the sample size, \( n \), is 39.
(b) Construct a 96% confidence interval about \( \mu \) if the sample size, \( n \), is 55. How does increasing the sample size affect the margin of error, \( E \)?
(c) Construct a 98% confidence interval about \( \mu \) if the sample size, \( n \), is 39. How does increasing the level of confidence affect the size of the margin of error, \( E \)?
(d) If the sample size is 19, what conditions must be satisfied to compute the confidence interval?
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**Solution for Part (a):**
(a) Construct a 96% confidence interval about \( \mu \) if the sample size, \( n \), is 39.
- **Lower bound:** [Input box]
- **Upper bound:** [Input box]
*Please round to two decimal places as needed.*
---
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**Action Buttons:**
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**Notes:**
- No graphs or diagrams are included in this problem.
- To input data, please use the interactive fields provided.
**Screen Information:**
- The laptop screen displays the mathematical problem and input fields for the confidence interval.
- There is a pink pencil in the foreground, suggesting that the image is being taken while solving the problem.
- The date and time on the bottom right corner of the screen indicate "12:38 PM, 06/17/2022".
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Transcribed Image Text:**Educational Website Transcription:**
---
**Topic: Constructing Confidence Intervals**
A simple random sample of size \( n \) is drawn from a population that is normally distributed. The sample mean, \( \overline{x} \), is found to be 17.7, and the sample standard deviation, \( s \), is found to be 4.3.
(a) Construct a 96% confidence interval about \( \mu \) if the sample size, \( n \), is 39.
(b) Construct a 96% confidence interval about \( \mu \) if the sample size, \( n \), is 55. How does increasing the sample size affect the margin of error, \( E \)?
(c) Construct a 98% confidence interval about \( \mu \) if the sample size, \( n \), is 39. How does increasing the level of confidence affect the size of the margin of error, \( E \)?
(d) If the sample size is 19, what conditions must be satisfied to compute the confidence interval?
---
**Solution for Part (a):**
(a) Construct a 96% confidence interval about \( \mu \) if the sample size, \( n \), is 39.
- **Lower bound:** [Input box]
- **Upper bound:** [Input box]
*Please round to two decimal places as needed.*
---
**Navigation Options:**
- Help me solve this
- View an example
- Get more help
**Action Buttons:**
- Clear all
- Check answer
**Notes:**
- No graphs or diagrams are included in this problem.
- To input data, please use the interactive fields provided.
**Screen Information:**
- The laptop screen displays the mathematical problem and input fields for the confidence interval.
- There is a pink pencil in the foreground, suggesting that the image is being taken while solving the problem.
- The date and time on the bottom right corner of the screen indicate "12:38 PM, 06/17/2022".
---
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