Translate the statement into a confidence interval. Approximate the level of confidence. In a survey of 1000 adults in a country, 65% said being able to speak the language is at the core of national identity. The survey's margin of error is +3.4%. The confidence interval for the proportion is ( D. (Round to three decimal places as needed.)

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
**Task: Translating Survey Results into a Confidence Interval**

**Objective:** Approximate the level of confidence from survey data.

**Survey Data:** 
- Sample size: 1000 adults 
- Proportion agreeing: 65% 
- Margin of error: ± 3.4%

**Instruction:** Calculate the confidence interval for the proportion.

**Calculation:**

1. **Proportion of agreement (p):** 65% or 0.65 
2. **Margin of error (E):** 3.4% or 0.034

**Confidence Interval Formula:** 
\[ \text{Confidence Interval} = (p - E, p + E) \]

**Calculation:**
\[ \text{Lower Bound} = 0.65 - 0.034 = 0.616 \]
\[ \text{Upper Bound} = 0.65 + 0.034 = 0.684 \]

**Final Confidence Interval:**
- The confidence interval for the proportion is (0.616, 0.684).

**Note:** Round your answer to three decimal places as needed. 

Enter your calculated confidence interval in the provided fields and click "Check Answer" to verify.
Transcribed Image Text:**Task: Translating Survey Results into a Confidence Interval** **Objective:** Approximate the level of confidence from survey data. **Survey Data:** - Sample size: 1000 adults - Proportion agreeing: 65% - Margin of error: ± 3.4% **Instruction:** Calculate the confidence interval for the proportion. **Calculation:** 1. **Proportion of agreement (p):** 65% or 0.65 2. **Margin of error (E):** 3.4% or 0.034 **Confidence Interval Formula:** \[ \text{Confidence Interval} = (p - E, p + E) \] **Calculation:** \[ \text{Lower Bound} = 0.65 - 0.034 = 0.616 \] \[ \text{Upper Bound} = 0.65 + 0.034 = 0.684 \] **Final Confidence Interval:** - The confidence interval for the proportion is (0.616, 0.684). **Note:** Round your answer to three decimal places as needed. Enter your calculated confidence interval in the provided fields and click "Check Answer" to verify.
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