(a) If researchers decide on a 4.2% margin of error for a 95% confidence interval. What sample size should they pursue? If researchers decide on a 2.8% margin of error for a 99% confidence interval. What sample size should they pursue?

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
Topic Video
Question
100%
Before conducting a study it is often a good idea to decide on the necessary sample size. To do so, statisticians often first decide on an
acceptable margin of error and then work backward to the sample size. Since they haven't run the study yet it is common practice to approximate the
sample proportion as 50% since this is the worst case scenario.
Recall that the standard eror for a single proportion is
SE =
P(1-p)
Note: The calculation to find the sample size will likely give a decimal answer so be sure to round appropriately so that the actual margin of error will be
less than what the researchers want.
(a) If researchers decide on a 4.2% margin of error for a 95% confidence interval. What sample size should they pursue?
(b) If researchers decide on a 2.8% margin of error for a 99% confidence interval. What sample size should they pursue?
Transcribed Image Text:Before conducting a study it is often a good idea to decide on the necessary sample size. To do so, statisticians often first decide on an acceptable margin of error and then work backward to the sample size. Since they haven't run the study yet it is common practice to approximate the sample proportion as 50% since this is the worst case scenario. Recall that the standard eror for a single proportion is SE = P(1-p) Note: The calculation to find the sample size will likely give a decimal answer so be sure to round appropriately so that the actual margin of error will be less than what the researchers want. (a) If researchers decide on a 4.2% margin of error for a 95% confidence interval. What sample size should they pursue? (b) If researchers decide on a 2.8% margin of error for a 99% confidence interval. What sample size should they pursue?
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps

Blurred answer
Knowledge Booster
Hypothesis Tests and Confidence Intervals for Means
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.
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