
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
expand_more
expand_more
format_list_bulleted
Concept explainers
Topic Video
Question
![### Estimating Sample Size for Population Proportion
To estimate a population proportion, you need to determine the appropriate sample size. Consider the following scenario:
**Scenario:**
- **Population Proportion (p):** Approximately 42%
- **Confidence Level:** 99%
- **Margin of Error:** 2.5%
**Question:**
How large of a sample size is required to ensure your estimate is within 2.5% of the true population proportion with 99% confidence?
**Hint:**
A linked video is provided to assist with this calculation.
**Input Field:**
You are prompted to input the calculated sample size (n) and submit your answer using the "Submit Question" button.
**Note:**
To calculate the sample size, you can use the formula for sample size estimation for proportions:
\[ n = \left( \frac{Z^2 \times p \times (1-p)}{E^2} \right) \]
Where:
- \( Z \) is the Z-score corresponding to the desired confidence level.
- \( p \) is the estimated population proportion.
- \( E \) is the margin of error.
This exercise helps learners apply statistical concepts to real-world data analysis scenarios.](https://content.bartleby.com/qna-images/question/6aae277d-04e7-4ff7-b330-5dc8e3941ab0/0bd8a345-ff05-4bb7-936b-04fec92885cb/mb1nrx_thumbnail.jpeg)
Transcribed Image Text:### Estimating Sample Size for Population Proportion
To estimate a population proportion, you need to determine the appropriate sample size. Consider the following scenario:
**Scenario:**
- **Population Proportion (p):** Approximately 42%
- **Confidence Level:** 99%
- **Margin of Error:** 2.5%
**Question:**
How large of a sample size is required to ensure your estimate is within 2.5% of the true population proportion with 99% confidence?
**Hint:**
A linked video is provided to assist with this calculation.
**Input Field:**
You are prompted to input the calculated sample size (n) and submit your answer using the "Submit Question" button.
**Note:**
To calculate the sample size, you can use the formula for sample size estimation for proportions:
\[ n = \left( \frac{Z^2 \times p \times (1-p)}{E^2} \right) \]
Where:
- \( Z \) is the Z-score corresponding to the desired confidence level.
- \( p \) is the estimated population proportion.
- \( E \) is the margin of error.
This exercise helps learners apply statistical concepts to real-world data analysis scenarios.
![Title: Determining Sample Size for Estimating a Population Mean
**Problem Statement:**
You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately \( \sigma = 76.9 \). You would like to be 95% confident that your estimate is within 5 of the true population mean. How large of a sample size is required?
**Interactive Element:**
- **Hint:**
- [Video] [](https://content.bartleby.com/qna-images/question/6aae277d-04e7-4ff7-b330-5dc8e3941ab0/0bd8a345-ff05-4bb7-936b-04fec92885cb/l45bj36_thumbnail.jpeg)
Transcribed Image Text:Title: Determining Sample Size for Estimating a Population Mean
**Problem Statement:**
You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately \( \sigma = 76.9 \). You would like to be 95% confident that your estimate is within 5 of the true population mean. How large of a sample size is required?
**Interactive Element:**
- **Hint:**
- [Video] [
Expert Solution

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 nowThis is a popular solution!
Step by stepSolved in 3 steps with 2 images

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.Similar questions
- You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately p∗=32%. You would like to be 95% confident that your esimate is within 2.5% of the true population proportion. How large of a sample size is required?n =arrow_forwardYou want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately 85%. You would like to be 99% confident that your estimate is within 4% of the true population proportion. How large of a sample size is required?arrow_forwardYou want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately 56%. You would like to be 99% confident that your estimate is within 2.5% of the true population proportion. How large of a sample size is required? > Next Questionarrow_forward
- You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately p=14%. You would like to be 99% confident that your estimate is within 4% of the true population proportion. How large of a sample size is required?arrow_forwardYou want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately 19%. You would like to be 99% confident that your estimate is within 4.5% of the true population proportion. How large of a sample size is required? Hint: Textbook Video (+] n =arrow_forwardYou want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately 68%. You would like to be 95% confident that your estimate is within 3.5% of the true population proportion. How large of a sample size is required? Do not round mid-calculation.arrow_forward
- You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportiòn is approximately 85%. You would like to be 99% confident that your estimate is within 2% of the true population proportion. How large of a sample size is required? Do not round mid-calculation. n =arrow_forwardYou want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately p∗=22%p∗=22%. You would like to be 95% confident that your esimate is within 4% of the true population proportion. How large of sample size is required?arrow_forwardYou want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately p∗=23%p∗=23%. You would like to be 98% confident that your esimate is within 3% of the true population proportion. How large of a sample size is required?n =arrow_forward
- You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately 42%. You would like to be 90% confident that your estimate is within 1.5% of the true population proportion. How large of a sample size is required? n =arrow_forwardYou want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately p∗=70%. You would like to be 90% confident that your esimate is within 0.5% of the true population proportion. How large of a sample size is required?n =arrow_forwardYou want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately 90%. You would like to be 95% confident that your estimate is within 2% of the true population proportion. How large of a sample size is required? n =arrow_forward
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
- MATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th...StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C...StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage Learning
- Elementary Statistics: Picturing the World (7th E...StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman

MATLAB: An Introduction with Applications
Statistics
ISBN:9781119256830
Author:Amos Gilat
Publisher:John Wiley & Sons Inc

Probability and Statistics for Engineering and th...
Statistics
ISBN:9781305251809
Author:Jay L. Devore
Publisher:Cengage Learning

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...
Statistics
ISBN:9780134683416
Author:Ron Larson, Betsy Farber
Publisher:PEARSON

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
Statistics
ISBN:9781319013387
Author:David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:W. H. Freeman