A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x, is found to be 109, and the sample standard deviation, s, is found to b (a) Construct a 96% confidence interval about μ if the sample size, n, is 21. (b) Construct a 96% confidence interval about µ if the sample size, n, is 14. (c) Construct a 95% confidence interval about μ if the sample size, n, is 21. (d) Should the confidence intervals in parts (a)-(c) have been computed if the population had not been normally distributed? (a) Construct a 96% confidence interval about μ if the sample size, n, is 21. Lower bound:: Upper bound: Round to one decimal place as needed.) (b) Construct a 96% confidence interval about μ if the sample size, n, is 14. Lower bound:; Upper bound: Round to one decimal place as needed.) How does decreasing the sample size affect the margin of error, E? OA. As the sample size decreases, the margin of error stays the same. OB. As the sample size decreases, the margin of error decreases. OC. As the sample size decreases, the margin of error increases. ... (c) Construct a 95% confidence interval about μ if the sample size, n, is 21. Lower bound:; Upper bound: (Round to one decimal place as needed.) Compare the results to those obtained in part (a). How does decreasing the level of confidence affect the size of the margin of error, E?

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Question
A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x, is found to be 109, and the sample standard deviation, s, is found to be 10.
(a) Construct a 96% confidence interval about µ if the sample size, n, is 21.
μ
(b) Construct a 96% confidence interval about µ if the sample size, n, is 14.
μ
(c) Construct a 95% confidence interval about μ if the sample size, n, is 21.
(d) Should the confidence intervals in parts (a)-(c) have been computed if the population had not been normally distributed?
(a) Construct a 96% confidence interval about µ if the sample size, n, is 21.
Lower bound: Upper bound:
(Round to one decimal place as needed.)
(b) Construct a 96% confidence interval about µ if the sample size, n, is 14.
μ
Lower bound:; Upper bound:
(Round to one decimal place as needed.)
How does decreasing the sample size affect the margin of error, E?
A. As the sample size decreases, the margin of error stays the same.
B. As the sample size decreases, the margin of error decreases.
C. As the sample size decreases, the margin of error increases.
(c) Construct a 95% confidence interval about µ if the sample size, n, is 21.
μ
Lower bound: Upper bound:
(Round to one decimal place as needed.)
Compare the results to those obtained in part (a). How does decreasing the level of confidence affect the size of the margin of error, E?
Transcribed Image Text:A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x, is found to be 109, and the sample standard deviation, s, is found to be 10. (a) Construct a 96% confidence interval about µ if the sample size, n, is 21. μ (b) Construct a 96% confidence interval about µ if the sample size, n, is 14. μ (c) Construct a 95% confidence interval about μ if the sample size, n, is 21. (d) Should the confidence intervals in parts (a)-(c) have been computed if the population had not been normally distributed? (a) Construct a 96% confidence interval about µ if the sample size, n, is 21. Lower bound: Upper bound: (Round to one decimal place as needed.) (b) Construct a 96% confidence interval about µ if the sample size, n, is 14. μ Lower bound:; Upper bound: (Round to one decimal place as needed.) How does decreasing the sample size affect the margin of error, E? A. As the sample size decreases, the margin of error stays the same. B. As the sample size decreases, the margin of error decreases. C. As the sample size decreases, the margin of error increases. (c) Construct a 95% confidence interval about µ if the sample size, n, is 21. μ Lower bound: Upper bound: (Round to one decimal place as needed.) Compare the results to those obtained in part (a). How does decreasing the level of confidence affect the size of the margin of error, E?
(c) Construct a 95% confidence interval about µ if the sample size, n, is 21.
Lower bound:; Upper bound:
(Round to one decimal place as needed.)
Compare the results to those obtained in part (a). How does decreasing the level of confidence affect the size of the margin of error, E?
A. As the level of confidence decreases, the size of the interval stays the same.
B. As the level of confidence decreases, the size of the interval increases.
OC. As the level of confidence decreases, the size of the interval decreases.
(d) Should the confidence intervals in parts (a)-(c) have been computed if the population had not been normally distributed?
A. No, the population needs to be normally distributed because each sample size is less than 30.
B. Yes, the population does not need to be normally distributed because each sample size is less than 30.
C. No, the population needs to be normally distributed because each sample size is large relative to their respective population sizes.
D. Yes, the population does not need to be normally distributed because each sample size is small relative to their respective population sizes.
Transcribed Image Text:(c) Construct a 95% confidence interval about µ if the sample size, n, is 21. Lower bound:; Upper bound: (Round to one decimal place as needed.) Compare the results to those obtained in part (a). How does decreasing the level of confidence affect the size of the margin of error, E? A. As the level of confidence decreases, the size of the interval stays the same. B. As the level of confidence decreases, the size of the interval increases. OC. As the level of confidence decreases, the size of the interval decreases. (d) Should the confidence intervals in parts (a)-(c) have been computed if the population had not been normally distributed? A. No, the population needs to be normally distributed because each sample size is less than 30. B. Yes, the population does not need to be normally distributed because each sample size is less than 30. C. No, the population needs to be normally distributed because each sample size is large relative to their respective population sizes. D. Yes, the population does not need to be normally distributed because each sample size is small relative to their respective population sizes.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 5 steps with 3 images

Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
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 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…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
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
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman