A certain forum reported that in a survey of 2006 American adults, 24% said they believed in astrology. (a) Calculate a confidence interval at the 99% confidence level for the proportion of all adult Americans who believe in astrology. (Round your answers to three decimal places.) Interpret the resulting interval. O we are 99% confident that this interval contains the true population mean. O we are 99% confident that this interval does not contain the true population mean. O we are 99% confident that the true population mean lies above this interval. O We are 99% confident that the true population mean lies below this interval. (b) What sample size would be required for the width of a 99% CI to be at most 0.05 irrespective of the value of p? (Round your answer up to the nearest integer.)
A certain forum reported that in a survey of 2006 American adults, 24% said they believed in astrology. (a) Calculate a confidence interval at the 99% confidence level for the proportion of all adult Americans who believe in astrology. (Round your answers to three decimal places.) Interpret the resulting interval. O we are 99% confident that this interval contains the true population mean. O we are 99% confident that this interval does not contain the true population mean. O we are 99% confident that the true population mean lies above this interval. O We are 99% confident that the true population mean lies below this interval. (b) What sample size would be required for the width of a 99% CI to be at most 0.05 irrespective of the value of p? (Round your answer up to the nearest integer.)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
Related questions
Question
Please solve the screenshot, thanks!!
![**Educational Text: Confidence Intervals in Statistics**
**Problem Statement:**
A certain forum reported that in a survey of 2006 American adults, 24% said they believed in astrology.
**Questions:**
(a) Calculate a confidence interval at the 99% confidence level for the proportion of all adult Americans who believe in astrology. (Round your answers to three decimal places.)
- ( [Input Box], [Input Box] )
**Interpret the resulting interval:**
- [ ] We are 99% confident that this interval contains the true population mean.
- [ ] We are 99% confident that this interval does not contain the true population mean.
- [ ] We are 99% confident that the true population mean lies above this interval.
- [x] We are 99% confident that the true population mean lies below this interval.
(b) What sample size would be required for the width of a 99% confidence interval (CI) to be at most 0.05 irrespective of the value of \( \hat{p} \)? (Round your answer up to the nearest integer.)
- [Input Box]
**Explanation:**
In part (a), you are asked to construct a confidence interval for the proportion of adults who believe in astrology. This involves statistical calculations to determine the range within which you are 99% confident the true proportion lies. The interpretation question asks you to assess which statement correctly describes the confidence interval.
The diagram provides options for interpreting the resulting interval, with the correct option already selected.
Part (b) involves determining the necessary sample size to achieve a specific confidence interval width. This relates to the precision of estimations and how sample size affects it.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F56945fae-aeca-4f60-8c3d-a266c334f238%2F74ba7fe2-7831-40d6-8b4b-9ed865c6f7aa%2Few2h6x7_processed.png&w=3840&q=75)
Transcribed Image Text:**Educational Text: Confidence Intervals in Statistics**
**Problem Statement:**
A certain forum reported that in a survey of 2006 American adults, 24% said they believed in astrology.
**Questions:**
(a) Calculate a confidence interval at the 99% confidence level for the proportion of all adult Americans who believe in astrology. (Round your answers to three decimal places.)
- ( [Input Box], [Input Box] )
**Interpret the resulting interval:**
- [ ] We are 99% confident that this interval contains the true population mean.
- [ ] We are 99% confident that this interval does not contain the true population mean.
- [ ] We are 99% confident that the true population mean lies above this interval.
- [x] We are 99% confident that the true population mean lies below this interval.
(b) What sample size would be required for the width of a 99% confidence interval (CI) to be at most 0.05 irrespective of the value of \( \hat{p} \)? (Round your answer up to the nearest integer.)
- [Input Box]
**Explanation:**
In part (a), you are asked to construct a confidence interval for the proportion of adults who believe in astrology. This involves statistical calculations to determine the range within which you are 99% confident the true proportion lies. The interpretation question asks you to assess which statement correctly describes the confidence interval.
The diagram provides options for interpreting the resulting interval, with the correct option already selected.
Part (b) involves determining the necessary sample size to achieve a specific confidence interval width. This relates to the precision of estimations and how sample size affects it.
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 now
This is a popular solution!
Step by step
Solved in 2 steps with 3 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.Recommended textbooks for you
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON