Math Problem Statement

For a confidence interval for a population parameter (e.g., the population mean) computed at a 99% confidence level, what proportion of all possible confidence intervals will contain the true parameter value?

Solution

The question asks for the proportion of all possible confidence intervals that will contain the true parameter value for a 99% confidence level.

Explanation:

The confidence level directly represents the proportion of confidence intervals that will contain the true parameter value in repeated sampling. For a 99% confidence level, this proportion is 99%, or 0.99, since confidence level indicates how confident we are that the interval will include the true value.

Final Answer:

0.99


Would you like further details or explanations?

Related Questions:

  1. What does a confidence interval represent in statistical terms?
  2. How is a confidence level different from a probability?
  3. Why is a 99% confidence level wider than a 95% confidence level?
  4. How does sample size affect the width of a confidence interval?
  5. What happens if the population standard deviation is unknown when calculating confidence intervals?

Tip:

Remember, increasing the confidence level (e.g., from 95% to 99%) reduces the likelihood of missing the true parameter but increases the width of the interval.

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Math Problem Analysis

Mathematical Concepts

Confidence Intervals
Confidence Level
Probability

Formulas

Proportion = Confidence Level (in decimal form)

Theorems

Definition of Confidence Level

Suitable Grade Level

Grades 10-12