The mean and standard deviation of a random sample of n measurements are equal to 33.1 and 3.6, respectively. a. Find a 95% confidence interval for u if n = 100. b. Find a 95% confidence interval for μ if n = 400. c. Find the widths of the confidence intervals found in parts a and b. What is the effect on the width of a confidence interval of quadrupling the sample size while holding the confidence coefficient fixed? a. The 95% confidence interval for μ if n = 100 is approximately (Round to three decimal places as needed.) b. The 95% confidence interval μ if n = 400 is approximately - (Round to three decimal places as needed.) C... c. Choose the correct answer below. OA. Quadrupling the sample size while holding the confidence coefficient fixed decreases the width of the confidence interval by a factor of 4. OB. Quadrupling the sample size while holding the confidence coefficient fixed increases the width of the confidence interval by a factor of 4. OC. Quadrupling the sample size while holding the confidence coefficient fixed does not affect the width of the confidence interval. OD. Quadrupling the sample size while holding the confidence coefficient fixed increases the width of the confidence interval by a factor of 2. OE. Quadrupling the sample size while holding the confidence coefficient fixed decreases the width of the confidence interval by a factor of 2.
The mean and standard deviation of a random sample of n measurements are equal to 33.1 and 3.6, respectively. a. Find a 95% confidence interval for u if n = 100. b. Find a 95% confidence interval for μ if n = 400. c. Find the widths of the confidence intervals found in parts a and b. What is the effect on the width of a confidence interval of quadrupling the sample size while holding the confidence coefficient fixed? a. The 95% confidence interval for μ if n = 100 is approximately (Round to three decimal places as needed.) b. The 95% confidence interval μ if n = 400 is approximately - (Round to three decimal places as needed.) C... c. Choose the correct answer below. OA. Quadrupling the sample size while holding the confidence coefficient fixed decreases the width of the confidence interval by a factor of 4. OB. Quadrupling the sample size while holding the confidence coefficient fixed increases the width of the confidence interval by a factor of 4. OC. Quadrupling the sample size while holding the confidence coefficient fixed does not affect the width of the confidence interval. OD. Quadrupling the sample size while holding the confidence coefficient fixed increases the width of the confidence interval by a factor of 2. OE. Quadrupling the sample size while holding the confidence coefficient fixed decreases the width of the confidence interval by a factor of 2.
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
![The mean and standard deviation of a random sample of n measurements are equal to 33.1 and 3.6, respectively.
a. Find a 95% confidence interval for u if n = 100.
b. Find a 95% confidence interval for u if n 400.
c. Find the widths of the confidence intervals found in parts a and b. What is the effect on the width of a confidence interval of quadrupling the sample size while holding the confidence
coefficient fixed?
a. The 95% confidence interval for μ if n = 100 is approximately ().
(Round to three decimal places as needed.)
b. The 95% confidence interval μ if n = 400 is approximately (
(Round to three decimal places as needed.)
c. Choose the correct answer below.
O A. Quadrupling the sample size while holding the confidence coefficient fixed decreases the width of the confidence interval by a factor of 4.
O B. Quadrupling the sample size while holding the confidence coefficient fixed increases the width of the confidence interval by a factor of 4.
OC. Quadrupling the sample size while holding the confidence coefficient fixed does not affect the width of the confidence interval.
O D. Quadrupling the sample size while holding the confidence coefficient fixed increases the width of the confidence interval by a factor of 2.
O E. Quadrupling the sample size while holding the confidence coefficient fixed decreases the width of the confidence interval by a factor of 2.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2910e309-4023-42bb-9437-090123672c12%2F6142a6f6-8d94-4c53-925e-59deed539dc6%2Fl1iibha_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The mean and standard deviation of a random sample of n measurements are equal to 33.1 and 3.6, respectively.
a. Find a 95% confidence interval for u if n = 100.
b. Find a 95% confidence interval for u if n 400.
c. Find the widths of the confidence intervals found in parts a and b. What is the effect on the width of a confidence interval of quadrupling the sample size while holding the confidence
coefficient fixed?
a. The 95% confidence interval for μ if n = 100 is approximately ().
(Round to three decimal places as needed.)
b. The 95% confidence interval μ if n = 400 is approximately (
(Round to three decimal places as needed.)
c. Choose the correct answer below.
O A. Quadrupling the sample size while holding the confidence coefficient fixed decreases the width of the confidence interval by a factor of 4.
O B. Quadrupling the sample size while holding the confidence coefficient fixed increases the width of the confidence interval by a factor of 4.
OC. Quadrupling the sample size while holding the confidence coefficient fixed does not affect the width of the confidence interval.
O D. Quadrupling the sample size while holding the confidence coefficient fixed increases the width of the confidence interval by a factor of 2.
O E. Quadrupling the sample size while holding the confidence coefficient fixed decreases the width of the confidence interval by a factor of 2.
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
Step 1: Determine the given information
For a random sample of
The sample mean,
And the sample standard deviation,
The objective is to obtain the confidence interval for
As the population variance,
Step by step
Solved in 3 steps with 2 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
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