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 (0.616 , 0.684 ). (Round to three decimal places as needed.) The interval is a % confidence interval. (Round to one decimal place 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
**Translating Survey Results to a Confidence Interval**

To better understand survey results, we often need to translate them into a confidence interval, allowing us to approximate the level of confidence we can have in the data. Here's an example:

**Survey Context**: A survey of 1000 adults in a country revealed that 65% of respondents believe speaking the national language is crucial to national identity. The survey's margin of error is ± 3.4%.

**Confidence Interval Calculation**:  
The margin of error is added and subtracted from the percentage to create a confidence interval. In this case:

- Lower limit: 65% - 3.4% = 61.6% (shown as 0.616 in decimal form)
- Upper limit: 65% + 3.4% = 68.4% (shown as 0.684 in decimal form)

Thus, the confidence interval for this proportion is (0.616, 0.684).

You are also asked to identify the confidence level of this interval. This step requires statistical methods or graphical tools to determine and would be expressed as a percentage. Typically, common confidence levels are 90%, 95%, or 99%. The exact level here needs to be calculated based on the statistical methodology or tools.

This approach aids in understanding the dispersion and reliability of survey data, offering a more nuanced picture of public opinion.
Transcribed Image Text:**Translating Survey Results to a Confidence Interval** To better understand survey results, we often need to translate them into a confidence interval, allowing us to approximate the level of confidence we can have in the data. Here's an example: **Survey Context**: A survey of 1000 adults in a country revealed that 65% of respondents believe speaking the national language is crucial to national identity. The survey's margin of error is ± 3.4%. **Confidence Interval Calculation**: The margin of error is added and subtracted from the percentage to create a confidence interval. In this case: - Lower limit: 65% - 3.4% = 61.6% (shown as 0.616 in decimal form) - Upper limit: 65% + 3.4% = 68.4% (shown as 0.684 in decimal form) Thus, the confidence interval for this proportion is (0.616, 0.684). You are also asked to identify the confidence level of this interval. This step requires statistical methods or graphical tools to determine and would be expressed as a percentage. Typically, common confidence levels are 90%, 95%, or 99%. The exact level here needs to be calculated based on the statistical methodology or tools. This approach aids in understanding the dispersion and reliability of survey data, offering a more nuanced picture of public opinion.
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