Math Problem Statement
A sample of voters were polled to determine the likelyhood of measure 324 passing. The poll determined that 40 % of voters were in favor of the measure with a margin of error of 3.4 %. Find the confidence interval. Use ( ) in your notation.
Solution
To find the confidence interval for the proportion of voters in favor of measure 324, we use the formula:
Where:
- (the sample proportion)
- Margin of error
Thus, the confidence interval is:
So, the confidence interval is:
Would you like further details on this, or any clarification?
Here are some related questions:
- What does the margin of error mean in this context?
- How is the confidence level related to the margin of error?
- How can the sample size affect the width of the confidence interval?
- What assumptions are made when calculating this confidence interval?
- How can we reduce the margin of error in future polls?
Tip: Increasing the sample size can reduce the margin of error, leading to a more precise confidence interval.
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Math Problem Analysis
Mathematical Concepts
Statistics
Confidence Interval
Margin of Error
Proportions
Formulas
Confidence Interval = (p̂ - Margin of Error, p̂ + Margin of Error)
Theorems
Central Limit Theorem
Normal Approximation for Proportions
Suitable Grade Level
Grades 10-12
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