Question Help In a survey of 3196 adults, 1447 say they have started paying bills online in the last year. Construct a 99% confidence interval for the population proportion. Interpret the results. A 99% confidence interval for the population proportion is D el (Round to three decimal places as needed.) Interpret your results. Choose the correct answer below. cic f edo O A. The endpoints of the given confidence interval show that adults pay bills online 99% of the time. O B. With 99% confidence, it can be said that the population proportion of adults who say they have started paying bills online in the last year is between the endpoints of the given confidence interval. +2.1 OC. With 99% confidence, it can be said that the sample proportion of adults who say they have started paying bills online in the last year is between the endpoints of the given confidence interval. m: e) u [2. e the pri ted, clic ode (0) More Check out Click to select your answer(s). eclick.net/pcs/c dh5q7L JUN O étv Aa
Question Help In a survey of 3196 adults, 1447 say they have started paying bills online in the last year. Construct a 99% confidence interval for the population proportion. Interpret the results. A 99% confidence interval for the population proportion is D el (Round to three decimal places as needed.) Interpret your results. Choose the correct answer below. cic f edo O A. The endpoints of the given confidence interval show that adults pay bills online 99% of the time. O B. With 99% confidence, it can be said that the population proportion of adults who say they have started paying bills online in the last year is between the endpoints of the given confidence interval. +2.1 OC. With 99% confidence, it can be said that the sample proportion of adults who say they have started paying bills online in the last year is between the endpoints of the given confidence interval. m: e) u [2. e the pri ted, clic ode (0) More Check out Click to select your answer(s). eclick.net/pcs/c dh5q7L JUN O étv Aa
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
Concept explainers
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
Topic Video
Question
![### Constructing and Interpreting a 99% Confidence Interval
**Problem Statement:**
In a survey of 3196 adults, 1447 say they have started paying bills online in the last year.
1. **Construct a 99% confidence interval for the population proportion. Interpret the results.**
2. **Task:** A 99% confidence interval for the population proportion is \( \big[ \ \ \big] \).
(Round to three decimal places as needed.)
3. **Interpret your results. Choose the correct answer below.**
**Options:**
A. The endpoints of the given confidence interval show that adults pay bills online 99% of the time.
B. With 99% confidence, it can be said that the population proportion of adults who say they have started paying bills online in the last year is between the endpoints of the given confidence interval.
C. With 99% confidence, it can be said that the sample proportion of adults who say they have started paying bills online in the last year is between the endpoints of the given confidence interval.
**Explanation of Steps and Concepts:**
1. **Identify the sample proportion (p-hat):**
- \( \hat{p} = \frac{\text{number of adults started paying bills online}}{\text{total number of adults surveyed}} \)
- \( \hat{p} = \frac{1447}{3196} \)
2. **Calculate the standard error (SE) for the proportion:**
- \( SE = \sqrt{\frac{\hat{p}(1 - \hat{p})}{n}} \)
- Where \( \hat{p} \) is the sample proportion and \( n \) is the sample size.
3. **Determine the z-value for a 99% confidence interval:**
- For a 99% confidence interval, the z-value (critical value) is 2.576.
4. **Construct the confidence interval:**
- \( \hat{p} \pm z \cdot SE \)
- This will give you the lower and upper bounds of the confidence interval.
5. **Interpret the interval:**
- The correct interpretation will explain the range within which the true population proportion likely falls, with 99% confidence.
**Correct Interpretation and Answer:**
Based on the provided options, the correct interpretation of a 99](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8d7dd878-68eb-4c6b-9d67-0903dd8963d8%2Fe870cdb0-e1f8-4fa8-927c-0327ba84d99b%2Fy169l1p_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Constructing and Interpreting a 99% Confidence Interval
**Problem Statement:**
In a survey of 3196 adults, 1447 say they have started paying bills online in the last year.
1. **Construct a 99% confidence interval for the population proportion. Interpret the results.**
2. **Task:** A 99% confidence interval for the population proportion is \( \big[ \ \ \big] \).
(Round to three decimal places as needed.)
3. **Interpret your results. Choose the correct answer below.**
**Options:**
A. The endpoints of the given confidence interval show that adults pay bills online 99% of the time.
B. With 99% confidence, it can be said that the population proportion of adults who say they have started paying bills online in the last year is between the endpoints of the given confidence interval.
C. With 99% confidence, it can be said that the sample proportion of adults who say they have started paying bills online in the last year is between the endpoints of the given confidence interval.
**Explanation of Steps and Concepts:**
1. **Identify the sample proportion (p-hat):**
- \( \hat{p} = \frac{\text{number of adults started paying bills online}}{\text{total number of adults surveyed}} \)
- \( \hat{p} = \frac{1447}{3196} \)
2. **Calculate the standard error (SE) for the proportion:**
- \( SE = \sqrt{\frac{\hat{p}(1 - \hat{p})}{n}} \)
- Where \( \hat{p} \) is the sample proportion and \( n \) is the sample size.
3. **Determine the z-value for a 99% confidence interval:**
- For a 99% confidence interval, the z-value (critical value) is 2.576.
4. **Construct the confidence interval:**
- \( \hat{p} \pm z \cdot SE \)
- This will give you the lower and upper bounds of the confidence interval.
5. **Interpret the interval:**
- The correct interpretation will explain the range within which the true population proportion likely falls, with 99% confidence.
**Correct Interpretation and Answer:**
Based on the provided options, the correct interpretation of a 99
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.
Step by step
Solved in 2 steps with 1 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