### 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.

It is given that, sample size, n =12 sample average, x̅ =82.2 and sample standard deviation, s= 7.1…

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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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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

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### 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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