6.16 More confidence interval mistakes and misunderstandings. Suppose that 100 randomly selected members of the Karaoke Channel were asked how much time they typically spend on the site during the week. The sample mean was found to be 3.8 hours. Assume that the population standard deviation is known to be o = 2.9. (a) Cary Oakey computes the 95% confidence interval for the average time on the site as 3.8 ± 1.96(2.9/100). What is his mistake? (b) He corrects this mistake and then states that "95% of the members spend between 3.23 and 4.37 hours a week on the site." What is wrong with his interpretation of this interval? (c) The margin of error is slightly larger than half an hour. To reduce this to roughly 15 minutes, Cary says that the sample size needs to be doubled to 200. What is wrong with this statement?
6.16 More confidence interval mistakes and misunderstandings. Suppose that 100 randomly selected members of the Karaoke Channel were asked how much time they typically spend on the site during the week. The sample mean was found to be 3.8 hours. Assume that the population standard deviation is known to be o = 2.9. (a) Cary Oakey computes the 95% confidence interval for the average time on the site as 3.8 ± 1.96(2.9/100). What is his mistake? (b) He corrects this mistake and then states that "95% of the members spend between 3.23 and 4.37 hours a week on the site." What is wrong with his interpretation of this interval? (c) The margin of error is slightly larger than half an hour. To reduce this to roughly 15 minutes, Cary says that the sample size needs to be doubled to 200. What is wrong with this statement?
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
Question
![6.16 More confidence interval mistakes and
misunderstandings. Suppose that 100 randomly selected
members of the Karaoke Channel were asked how much
time they typically spend on the site during the week. The
sample mean it was found to be 3.8 hours. Assume that
the population standard deviation is known to be o = 2.9.
(a) Cary Oakey computes the 95% confidence interval for
the average time on the site as 3.8 ± 1.96(2.9/100). What
is his mistake?
(b) He corrects this mistake and then states that "95% of
the members spend between 3.23 and 4.37 hours a week
on the site." What is wrong with his interpretation of this
interval?
(c) The margin of error is slightly larger than half an
hour. To reduce this to roughly 15 minutes, Cary says
that the sample size needs to be doubled to 200. What is
wrong with this statement?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F44b767e2-6751-4234-b8c8-6ae85db4f11d%2F20a17370-7fc9-4965-8934-0865ff45045b%2Fkzqboa_processed.jpeg&w=3840&q=75)
Transcribed Image Text:6.16 More confidence interval mistakes and
misunderstandings. Suppose that 100 randomly selected
members of the Karaoke Channel were asked how much
time they typically spend on the site during the week. The
sample mean it was found to be 3.8 hours. Assume that
the population standard deviation is known to be o = 2.9.
(a) Cary Oakey computes the 95% confidence interval for
the average time on the site as 3.8 ± 1.96(2.9/100). What
is his mistake?
(b) He corrects this mistake and then states that "95% of
the members spend between 3.23 and 4.37 hours a week
on the site." What is wrong with his interpretation of this
interval?
(c) The margin of error is slightly larger than half an
hour. To reduce this to roughly 15 minutes, Cary says
that the sample size needs to be doubled to 200. What is
wrong with this statement?
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 3 steps with 3 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Follow-up Questions
Read through expert solutions to related follow-up questions below.
Follow-up Question
does question say to bring the sample donw by 1/2 or the mean down by 1/2
Solution
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