Math Problem Statement
c. Find a 95% confidence interval for the proportion of adults in the country who believe that protecting the rights of those with unpopular views is a very important component of a strong democracy. The 95% confidence interval is (
enter your response here,
enter your response here). (Round to three decimal places as needed.)
Solution
To find the 95% confidence interval for the proportion of adults in the country who believe that protecting the rights of those with unpopular views is a very important component of a strong democracy, we need the following information:
- The sample proportion ()
- The sample size ()
The formula for the confidence interval for a proportion is:
where:
- is the sample proportion
- is the critical value from the standard normal distribution for a 95% confidence level, which is 1.96
- is the sample size
Let's assume we have the sample proportion and sample size:
- (example value)
- (example value)
Now, we can calculate the standard error (SE):
Next, we find the margin of error (ME):
Finally, we can calculate the confidence interval:
So, the 95% confidence interval is:
Please adjust the values of and to your specific problem's data.
Would you like further details or have any questions?
Here are five questions you might ask next:
- How do I determine the sample proportion () from my data?
- What is the critical value for a 99% confidence interval?
- How does sample size affect the width of the confidence interval?
- Can you explain the concept of standard error in more detail?
- How do I interpret this confidence interval in the context of my data?
Tip: The larger your sample size, the narrower your confidence interval will be, providing a more precise estimate of the population proportion.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Statistics
Confidence Intervals
Sampling
Formulas
Confidence interval formula for proportions
Theorems
-
Suitable Grade Level
Advanced High School
Related Recommendation
95% Confidence Interval for Proportion of Voters Against School Bonds
Calculate Confidence Intervals for True Proportions: Dr. Archer vs. Dr. Budden
Estimate Proportion of Australians Who Believe Unemployment Will Increase
95% Confidence Interval for Proportion of People Who Like Dogs
Estimating Proportion for Study Abroad Program Participation with 99% Confidence