Math Problem Statement
The mean was found to be 23% and the confidence interval was (19.7%,26.3%) therefore the margin of error was +/- _____%.
Solution
The margin of error (ME) can be found by calculating the difference between the mean and one of the bounds of the confidence interval.
Given:
- Mean = 23%
- Confidence Interval = (19.7%, 26.3%)
The margin of error is calculated as:
Let's calculate:
Or:
Thus, the margin of error is ±3.3%.
Would you like more details, or do you have any questions?
Here are 5 related questions you might consider:
- How is the confidence interval interpreted in terms of population parameters?
- What is the significance of a 95% confidence level in confidence intervals?
- How do sample size and variability affect the margin of error?
- How can you decrease the margin of error in a study?
- What is the difference between a one-sided and a two-sided confidence interval?
Tip: The margin of error decreases as the sample size increases, which is why larger studies tend to produce more precise estimates.
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Math Problem Analysis
Mathematical Concepts
Statistics
Confidence Intervals
Margin of Error
Formulas
Margin of Error = Upper Bound - Mean or Mean - Lower Bound
Theorems
Confidence Interval Theorem
Suitable Grade Level
Grades 10-12
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