(a) Construct a 95% confidence interval about if the sample size, n, is 35. Lower bound: 16.75; Upper bound: 20.05 (Use ascending order. Round to two decimal places as needed.) (b) Construct a 95% confidence interval about μ if the sample size, n, is 61. Lower bound: 17.17; Upper bound: 19.63 (Use ascending order. Round to two decimal places as needed.)
(a) Construct a 95% confidence interval about if the sample size, n, is 35. Lower bound: 16.75; Upper bound: 20.05 (Use ascending order. Round to two decimal places as needed.) (b) Construct a 95% confidence interval about μ if the sample size, n, is 61. Lower bound: 17.17; Upper bound: 19.63 (Use ascending order. Round to two decimal places as needed.)
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
![A simple random sample of size n is drawn. The sample mean, \(\bar{x}\), is found to be 18.4, and the sample standard deviation, s, is found to be 4.8.
- A link is provided to view the table of areas under the t-distribution.
---
### (a)
Construct a 95% confidence interval about \(\mu\) if the sample size, n, is 35.
- **Lower bound:** 16.75; **Upper bound:** 20.05
*(Use ascending order. Round to two decimal places as needed.)*
### (b)
Construct a 95% confidence interval about \(\mu\) if the sample size, n, is 61.
- **Lower bound:** 17.17; **Upper bound:** 19.63
*(Use ascending order. Round to two decimal places as needed.)*
- **Question:** How does increasing the sample size affect the margin of error, E?
- **A.** The margin of error increases.
- **B.** The margin of error decreases. *(Correct)*
- **C.** The margin of error does not change.
### (c)
Construct a 99% confidence interval about \(\mu\) if the sample size, n, is 35.
- **Lower bound:** [ ]
- **Upper bound:** [ ]
*(Use ascending order. Round to two decimal places as needed.)*](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fac3be618-b645-4bd8-855b-808ff3fc18d4%2Fb65ae8aa-ec8e-432d-946c-bf08a8fc5f26%2Faq78h7_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A simple random sample of size n is drawn. The sample mean, \(\bar{x}\), is found to be 18.4, and the sample standard deviation, s, is found to be 4.8.
- A link is provided to view the table of areas under the t-distribution.
---
### (a)
Construct a 95% confidence interval about \(\mu\) if the sample size, n, is 35.
- **Lower bound:** 16.75; **Upper bound:** 20.05
*(Use ascending order. Round to two decimal places as needed.)*
### (b)
Construct a 95% confidence interval about \(\mu\) if the sample size, n, is 61.
- **Lower bound:** 17.17; **Upper bound:** 19.63
*(Use ascending order. Round to two decimal places as needed.)*
- **Question:** How does increasing the sample size affect the margin of error, E?
- **A.** The margin of error increases.
- **B.** The margin of error decreases. *(Correct)*
- **C.** The margin of error does not change.
### (c)
Construct a 99% confidence interval about \(\mu\) if the sample size, n, is 35.
- **Lower bound:** [ ]
- **Upper bound:** [ ]
*(Use ascending order. Round to two decimal places as needed.)*
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Transcribed Image Text:**Question:**
Compare the results to those obtained in part (a). How does increasing the level of confidence affect the size of the margin of error, E?
**Options:**
- **A.** The margin of error increases.
- **B.** The margin of error does not change.
- **C.** The margin of error decreases.
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