Math Problem Statement
Solution
The question asks for the correct interpretation of a 99% confidence interval, such as .
The correct answer is:
C. We are 99% confident that the interval from 4.1 to 5.6 actually does contain the true value of .
Explanation:
In the context of confidence intervals, a 99% confidence level means that if we were to repeat the sampling process many times, approximately 99% of the intervals we calculate would contain the true population mean, . It does not mean that there is a 99% probability that is within the specific interval calculated from one sample.
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Related Questions:
- How would a 95% confidence interval differ in interpretation from a 99% confidence interval?
- Why is option B incorrect in this context?
- Can we interpret a confidence interval as a probability statement about ?
- What does a confidence level mean in practical terms?
- How does sample size affect the width of a confidence interval?
Tip:
Remember, a confidence interval provides an estimate of the range in which the true parameter lies, not a probability of where it lies based on one interval.
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Math Problem Analysis
Mathematical Concepts
Confidence Interval
Probability
Statistical Inference
Formulas
Confidence Interval = Sample Mean ± (Z-score * Standard Error)
Theorems
Central Limit Theorem
Suitable Grade Level
Undergraduate Statistics