Stats: Modeling the World Nasta Edition Grades 9-12
Stats: Modeling the World Nasta Edition Grades 9-12
3rd Edition
ISBN: 9780131359581
Author: David E. Bock, Paul F. Velleman, Richard D. De Veaux
Publisher: PEARSON
bartleby

Concept explainers

bartleby

Videos

Question
Book Icon
Chapter PV, Problem 10RE

(a)

To determine

To create a 95% confidence interval for the percentage of all American adults who favour the death penalty.

(a)

Expert Solution
Check Mark

Answer to Problem 10RE

  (0.428,0.512) .

Explanation of Solution

It is given in the question that of those polled, 47% chose the death penalty, the lowest percentage in the 21 years that Gallup has asked the question given. It is also given,

  p=0.47n=537c=0.95=95%

So, the standard error can be calculated as:

  SE=0.47(10.47)537=0.022

And for a 95% confidence level, z=1.96 , so,

  ME=z×SE=1.96×0.022=0.042

So, the 95% confidence interval is:

  0.47±(1.96×0.042)=(0.428,0.512)

Thus, 95% confidence interval for the percentage of all American adults who favour the death penalty is (0.428,0.512) .

(b)

To determine

To explain is it clear that the death penalty no longer has majority support.

(b)

Expert Solution
Check Mark

Answer to Problem 10RE

No, it is not clear.

Explanation of Solution

It is given in the question that of those polled, 47% chose the death penalty, the lowest percentage in the 21 years that Gallup has asked the question given. Thus, we can say that it is not clear that the death penalty no longer has majority support because the confidence interval contains values that would indicate majority support.

(c)

To determine

To find out how many people should they poll.

(c)

Expert Solution
Check Mark

Answer to Problem 10RE

  3381 people they should poll.

Explanation of Solution

It is given in the question that of those polled, 47% chose the death penalty, the lowest percentage in the 21 years that Gallup has asked the question given. Thus, if pollsters wanted to follow up on this poll worth another survey that could determine the level of support for the death penalty to within 2% with 98% confidence, then,

  0.02=2.33×0.47(10.47)n0.0004=5.4289×47.53nn=3381

Thus, 3381 people they should poll if pollsters wanted to follow up on this poll worth another survey that could determine the level of support for the death penalty to within 2% with 98% confidence.

Knowledge Booster
Background pattern image
Statistics
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.
Recommended textbooks for you
Text book image
MATLAB: An Introduction with Applications
Statistics
ISBN:9781119256830
Author:Amos Gilat
Publisher:John Wiley & Sons Inc
Text book image
Probability and Statistics for Engineering and th...
Statistics
ISBN:9781305251809
Author:Jay L. Devore
Publisher:Cengage Learning
Text book image
Statistics for The Behavioral Sciences (MindTap C...
Statistics
ISBN:9781305504912
Author:Frederick J Gravetter, Larry B. Wallnau
Publisher:Cengage Learning
Text book image
Elementary Statistics: Picturing the World (7th E...
Statistics
ISBN:9780134683416
Author:Ron Larson, Betsy Farber
Publisher:PEARSON
Text book image
The Basic Practice of Statistics
Statistics
ISBN:9781319042578
Author:David S. Moore, William I. Notz, Michael A. Fligner
Publisher:W. H. Freeman
Text book image
Introduction to the Practice of Statistics
Statistics
ISBN:9781319013387
Author:David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:W. H. Freeman
Hypothesis Testing - Solving Problems With Proportions; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=76VruarGn2Q;License: Standard YouTube License, CC-BY
Hypothesis Testing and Confidence Intervals (FRM Part 1 – Book 2 – Chapter 5); Author: Analystprep;https://www.youtube.com/watch?v=vth3yZIUlGQ;License: Standard YouTube License, CC-BY