5. On pages 20 to 22 on chapter 6 notes, the topic is how to calculate how large a sample must be to achieve a given confidence level and a given error distance. Suppose we are given the following information. No prior proportions are known, and the formula gives n = 432.41. On page 21 is an example that is worked two different ways. Use this example to decide which option below is most accurate for this situation? Use part (a) method and the correctly rounded value is n = 432 Use part (b) method and the correctly rounded value is n = 433 Use part (b) method and the correctly rounded value is n = 432 Use part (a) method and the correctly rounded value is n = 433

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

Hi, I added a picture of the notes in reference to the question. I appreciate the help, thanks

Example
Many companies are interested in knowing the percentage of adults who buy
clothing online.
How many adults must be surveyed in order to be 95% confident that the sample
percentage is in error by no more than three percentage points?
a.
b.
solution (a)
b)
Use a recent result from the Census Bureau: 66% of adults buy clothing
online.
Assume that we have no prior information suggesting a possible value of the
proportion.
n =
n =
p=0.66 and q = 1- p=0.34
α = 0.05 so Zα/2 = 1.96
E = 0.03
(Zu/2)²³ pâ
E²
(1.96)² (0.66)(0.34)
(0.03)²
= 957.839
= 958
a = 0.05 so Za/2
E = 0.03
(Zaz)².0.25
E²
(1.96)² -0.25
(0.03)²
= 1067.1111
= 1068
1.96
To be 95% confident that
our sample percentage is
within three percentage
points of the true
percentage for all adults,
we should obtain a simple
random sample of 958
adults.
To be 95% confident that
our sample percentage is
within three percentage
points of the true
percentage for all adults,
we should obtain a simple
random sample of 1068
adults.
Transcribed Image Text:Example Many companies are interested in knowing the percentage of adults who buy clothing online. How many adults must be surveyed in order to be 95% confident that the sample percentage is in error by no more than three percentage points? a. b. solution (a) b) Use a recent result from the Census Bureau: 66% of adults buy clothing online. Assume that we have no prior information suggesting a possible value of the proportion. n = n = p=0.66 and q = 1- p=0.34 α = 0.05 so Zα/2 = 1.96 E = 0.03 (Zu/2)²³ pâ E² (1.96)² (0.66)(0.34) (0.03)² = 957.839 = 958 a = 0.05 so Za/2 E = 0.03 (Zaz)².0.25 E² (1.96)² -0.25 (0.03)² = 1067.1111 = 1068 1.96 To be 95% confident that our sample percentage is within three percentage points of the true percentage for all adults, we should obtain a simple random sample of 958 adults. To be 95% confident that our sample percentage is within three percentage points of the true percentage for all adults, we should obtain a simple random sample of 1068 adults.
5. On pages 20 to 22 on chapter 6 notes, the topic is how to calculate how
large a sample must be to achieve a given confidence level and a given error
distance. Suppose we are given the following information. No prior
proportions are known, and the formula gives n = 432.41. On page 21 is an
example that is worked two different ways. Use this example to decide which
option below is most accurate for this situation?
Use part (a) method and the correctly rounded value is n = 432
Use part (b) method and the correctly rounded value is n = 433
Use part (b) method and the correctly rounded value is n = 432
Use part (a) method and the correctly rounded value is n = 433
Transcribed Image Text:5. On pages 20 to 22 on chapter 6 notes, the topic is how to calculate how large a sample must be to achieve a given confidence level and a given error distance. Suppose we are given the following information. No prior proportions are known, and the formula gives n = 432.41. On page 21 is an example that is worked two different ways. Use this example to decide which option below is most accurate for this situation? Use part (a) method and the correctly rounded value is n = 432 Use part (b) method and the correctly rounded value is n = 433 Use part (b) method and the correctly rounded value is n = 432 Use part (a) method and the correctly rounded value is n = 433
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps

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