Enter your answer in the edit fields and then click Check Answer. All parts showing Clear All
Enter your answer in the edit fields and then click Check Answer. All parts showing Clear All
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
100%
- [Page 2 of the standard normal distribution table](#)
- [Page 1 of the table of critical values of the t-distribution](#)
**Confidence Interval Calculation:**
The confidence interval is given by:
\[ \bar{x} \pm t \left( \frac{s}{\sqrt{n}} \right) \]
Where:
- \(\bar{x}\) is the sample mean
- \(t\) is the t-value from the t-distribution for \(n-1\) degrees of freedom and the specified confidence level
- \(s\) is the sample standard deviation
- \(n\) is the sample size
**Formula for this Problem:**
\[ 82.2 \pm t_{0.005, 11} \left( \frac{7.1}{\sqrt{12}} \right) \]
**Confidence Interval Result:**
The confidence interval is [ , ] (Round to two decimal places as needed.)
**Interactive Component:**
Enter your answer in the edit fields and then click **Check Answer**.
[Check Answer Button]
#### Additional Instructions:
- Use the provided links to access the necessary tables for standard normal distribution and t-distribution critical values.
- Ensure your final answer is rounded to two decimal places.
**Graphical Representation:**
While the image does not contain an explicit graph or diagram, the values needed to complete the calculation (standard deviation, sample mean, sample size, and confidence level) are provided.
---
**Note for Users:**
This exercise demonstrates how to compute a confidence interval for a sample mean when the population standard deviation is unknown and the sample size is small (n < 30). This requires the use of the t-distribution, a critical concept in inferential statistics.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F00702f10-6eb4-4090-beb7-8b014874b024%2F1ca586ff-0d5e-462a-b149-217572e10037%2Fm6epks_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Confidence Interval for Average Typing Speed of Secretarial School Graduates
**Problem Statement:**
A random sample of 12 graduates of a certain secretarial school typed an average of 82.2 words per minute with a standard deviation of 7.1 words per minute. Assuming a normal distribution for the number of words typed per minute, determine a 99% confidence interval for the average number of words typed by all graduates of this school.
**Resources Provided:**
- [Page 1 of the standard normal distribution table](#)
- [Page 2 of the standard normal distribution table](#)
- [Page 1 of the table of critical values of the t-distribution](#)
**Confidence Interval Calculation:**
The confidence interval is given by:
\[ \bar{x} \pm t \left( \frac{s}{\sqrt{n}} \right) \]
Where:
- \(\bar{x}\) is the sample mean
- \(t\) is the t-value from the t-distribution for \(n-1\) degrees of freedom and the specified confidence level
- \(s\) is the sample standard deviation
- \(n\) is the sample size
**Formula for this Problem:**
\[ 82.2 \pm t_{0.005, 11} \left( \frac{7.1}{\sqrt{12}} \right) \]
**Confidence Interval Result:**
The confidence interval is [ , ] (Round to two decimal places as needed.)
**Interactive Component:**
Enter your answer in the edit fields and then click **Check Answer**.
[Check Answer Button]
#### Additional Instructions:
- Use the provided links to access the necessary tables for standard normal distribution and t-distribution critical values.
- Ensure your final answer is rounded to two decimal places.
**Graphical Representation:**
While the image does not contain an explicit graph or diagram, the values needed to complete the calculation (standard deviation, sample mean, sample size, and confidence level) are provided.
---
**Note for Users:**
This exercise demonstrates how to compute a confidence interval for a sample mean when the population standard deviation is unknown and the sample size is small (n < 30). This requires the use of the t-distribution, a critical concept in inferential statistics.
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