Q4(ch 9). The libraries around the country face a crisis, the patrons now have so many choices to borrow a book in person becoming outdated Budget cuts around many libraries are becoming slated. Only 57% of patrons borrow books anymore, Claims the American Library Association, suddenly! This statistic is wrong to its core thinks the director of the library in Plainsboro, Kentucky. She hires a stats wizard to conduct a study. He did his thing and what did he find! That in Plainsboro many a person and their buddy Borrowed books to expand their mind. Of the 250 people he sampled with diligence, about 185 borrowed actual books with no indifference. Using a 1% level of significance, he made a report To show that the library was not falling short He calculated the possible proportion of patrons, loyally Borrowing books in good ol' Plainsboro, Kentucky! a. Find the standard Error . b. Find the Margin Error (ME) c. What is the Confidence interval = mean +/-ME
Q4(ch 9). The libraries around the country face a crisis, the patrons now have so many choices to borrow a book in person becoming outdated Budget cuts around many libraries are becoming slated. Only 57% of patrons borrow books anymore, Claims the American Library Association, suddenly! This statistic is wrong to its core thinks the director of the library in Plainsboro, Kentucky. She hires a stats wizard to conduct a study. He did his thing and what did he find! That in Plainsboro many a person and their buddy Borrowed books to expand their mind. Of the 250 people he sampled with diligence, about 185 borrowed actual books with no indifference. Using a 1% level of significance, he made a report To show that the library was not falling short He calculated the possible proportion of patrons, loyally Borrowing books in good ol' Plainsboro, Kentucky! a. Find the standard Error . b. Find the Margin Error (ME) c. What is the Confidence interval = mean +/-ME
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
Topic Video
Question
Hello,
Need steps and answers pls.
ty
![### Statistical Analysis of Borrowing Habits at Plainsboro Library
#### Study Overview
**Problem Context:**
The libraries across the country are facing a crisis with the increasing number of patrons opting for alternatives to borrowing books in person. Budget cuts are contributing to the decline of many libraries. According to the American Library Association, only 57% of patrons borrow books nowadays. However, the library director in Plainsboro, Kentucky, is skeptical of this statistic and hires a statistics expert to conduct a detailed study.
**Research Findings:**
The expert surveyed a sample of 250 people and found that 185 of them actually borrowed books. This study was conducted with a 1% level of significance.
#### Analyzing the Data
**a. Find the standard error:**
\[ \text{Standard Error (SE)} = \sqrt{\frac{p(1-p)}{n}} \]
Where:
- \( p \) is the sample proportion
- \( n \) is the sample size
**b. Find the Margin of Error (ME):**
\[ \text{Margin of Error (ME)} = z \times SE \]
Where \( z \) is the z-score corresponding to the desired confidence level
**c. Calculate the Confidence Interval:**
\[ \text{Confidence Interval} = \text{mean} \pm \text{Margin of Error (ME)} \]
#### Detailed Explanation:
1. **Sample Proportion (p):**
\[ p = \frac{185}{250} = 0.74 \]
2. **Standard Error (SE):**
Using the sample proportion \( p \) and sample size \( n = 250 \),
\[ SE = \sqrt{\frac{0.74 \times (1 - 0.74)}{250}} \]
3. **Z-Score for 1% Level of Significance:**
The z-score for a 99% confidence level (1% significance level) typically approximates to 2.576.
4. **Margin of Error (ME):**
\[ ME = 2.576 \times SE \]
5. **Confidence Interval:**
The confidence interval can be calculated using the sample mean:
\[ \text{95% Confidence Interval} = 0.74 \pm \text{ME} \]
This detailed analysis helps in understanding the library's borrowing habits and to determine whether the American Library](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc13bfa47-d8b1-49a8-8652-3d3d8ccb6fe9%2F6821078f-91c0-4344-90e1-ef730d1ccdb0%2Funioz6_processed.png&w=3840&q=75)
Transcribed Image Text:### Statistical Analysis of Borrowing Habits at Plainsboro Library
#### Study Overview
**Problem Context:**
The libraries across the country are facing a crisis with the increasing number of patrons opting for alternatives to borrowing books in person. Budget cuts are contributing to the decline of many libraries. According to the American Library Association, only 57% of patrons borrow books nowadays. However, the library director in Plainsboro, Kentucky, is skeptical of this statistic and hires a statistics expert to conduct a detailed study.
**Research Findings:**
The expert surveyed a sample of 250 people and found that 185 of them actually borrowed books. This study was conducted with a 1% level of significance.
#### Analyzing the Data
**a. Find the standard error:**
\[ \text{Standard Error (SE)} = \sqrt{\frac{p(1-p)}{n}} \]
Where:
- \( p \) is the sample proportion
- \( n \) is the sample size
**b. Find the Margin of Error (ME):**
\[ \text{Margin of Error (ME)} = z \times SE \]
Where \( z \) is the z-score corresponding to the desired confidence level
**c. Calculate the Confidence Interval:**
\[ \text{Confidence Interval} = \text{mean} \pm \text{Margin of Error (ME)} \]
#### Detailed Explanation:
1. **Sample Proportion (p):**
\[ p = \frac{185}{250} = 0.74 \]
2. **Standard Error (SE):**
Using the sample proportion \( p \) and sample size \( n = 250 \),
\[ SE = \sqrt{\frac{0.74 \times (1 - 0.74)}{250}} \]
3. **Z-Score for 1% Level of Significance:**
The z-score for a 99% confidence level (1% significance level) typically approximates to 2.576.
4. **Margin of Error (ME):**
\[ ME = 2.576 \times SE \]
5. **Confidence Interval:**
The confidence interval can be calculated using the sample mean:
\[ \text{95% Confidence Interval} = 0.74 \pm \text{ME} \]
This detailed analysis helps in understanding the library's borrowing habits and to determine whether the American Library
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 5 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.Recommended textbooks for you
![MATLAB: An Introduction with Applications](https://www.bartleby.com/isbn_cover_images/9781119256830/9781119256830_smallCoverImage.gif)
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
![Probability and Statistics for Engineering and th…](https://www.bartleby.com/isbn_cover_images/9781305251809/9781305251809_smallCoverImage.gif)
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
![Statistics for The Behavioral Sciences (MindTap C…](https://www.bartleby.com/isbn_cover_images/9781305504912/9781305504912_smallCoverImage.gif)
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
![MATLAB: An Introduction with Applications](https://www.bartleby.com/isbn_cover_images/9781119256830/9781119256830_smallCoverImage.gif)
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
![Probability and Statistics for Engineering and th…](https://www.bartleby.com/isbn_cover_images/9781305251809/9781305251809_smallCoverImage.gif)
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
![Statistics for The Behavioral Sciences (MindTap C…](https://www.bartleby.com/isbn_cover_images/9781305504912/9781305504912_smallCoverImage.gif)
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
![Elementary Statistics: Picturing the World (7th E…](https://www.bartleby.com/isbn_cover_images/9780134683416/9780134683416_smallCoverImage.gif)
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
![The Basic Practice of Statistics](https://www.bartleby.com/isbn_cover_images/9781319042578/9781319042578_smallCoverImage.gif)
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
![Introduction to the Practice of Statistics](https://www.bartleby.com/isbn_cover_images/9781319013387/9781319013387_smallCoverImage.gif)
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman