Math Problem Statement
How many voters should be sampled 95 % for a confidence interval? Round up to a whole number. A poll reported a approval rating 36% for a politician with a margin of error of 1 percentage point.
Solution
To determine the required sample size for a confidence interval, you can use the following formula for estimating proportions:
Where:
- is the Z-score for a 95% confidence level (which is 1.96),
- is the estimated proportion of the population, which is 36% or 0.36,
- is the margin of error, which is 1% or 0.01.
Let's calculate the sample size:
I'll compute that for you.The required sample size for the poll to achieve a 95% confidence interval with a 1 percentage point margin of error is approximately 8,852 voters.
Would you like more details or have any further questions?
Here are 5 related questions to expand on this concept:
- How does the margin of error affect the required sample size?
- What is the significance of the 95% confidence level in polls?
- How would the sample size change with a different margin of error?
- Why is it necessary to round up the sample size in such calculations?
- How does the estimated proportion (36% in this case) influence the sample size?
Tip: A larger sample size reduces the margin of error, increasing the accuracy of poll results.
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Math Problem Analysis
Mathematical Concepts
Statistics
Confidence Interval
Sample Size Estimation
Proportion
Formulas
n = (Z^2 * p * (1 - p)) / E^2
Theorems
Normal Distribution
Central Limit Theorem
Suitable Grade Level
College-Level Statistics
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