Math Problem Statement
What is the effect of increasing the level of confidence on the width of the interval?
Increasing the confidence level makes the interval (wider or narrower)
Solution
Increasing the confidence level makes the confidence interval wider.
Explanation:
- A higher confidence level means you want to be more certain that the interval contains the true population parameter.
- To achieve this increased certainty, the interval must cover a larger range of values, making it wider.
This trade-off occurs because increasing the confidence level reduces the risk of missing the true value (Type I error), but at the cost of precision (a narrower range).
Would you like a detailed example or further clarification?
Related Questions:
- How does sample size affect the width of a confidence interval?
- What is the relationship between confidence level and margin of error?
- Why does increasing confidence level reduce precision in statistical estimates?
- What are the practical implications of using a very wide confidence interval?
- How can confidence intervals be calculated for a population mean?
Tip: A higher confidence level increases the interval width, but a larger sample size can help counteract this by narrowing the interval.
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Math Problem Analysis
Mathematical Concepts
Statistics
Confidence Intervals
Formulas
Confidence Interval Formula: CI = Estimate ± Margin of Error
Margin of Error: ME = Z * (σ/√n)
Theorems
Properties of Confidence Intervals
Suitable Grade Level
Grades 10-12 and Introductory College Level
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