Math Problem Statement

Which of the following would be a correct interpretation of a 99% confidence interval such as 4.1 < μ < 5.6? Choose the correct answer from the following options: A) It means that 99% of all data values are between 4.1 and 5.6. B) There is a 99% chance that μ will fall between 4.1 and 5.6. C) We are 99% confident that the interval from 4.1 to 5.6 actually does contain the true value of μ. D) It means that 99% of sample means fall between 4.1 and 5.6.

Solution

The question asks for the correct interpretation of a 99% confidence interval, such as 4.1<μ<5.64.1 < \mu < 5.6.

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 μ\mu.

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, μ\mu. It does not mean that there is a 99% probability that μ\mu is within the specific interval calculated from one sample.

Let me know if you'd like more details or if you have questions!


Related Questions:

  1. How would a 95% confidence interval differ in interpretation from a 99% confidence interval?
  2. Why is option B incorrect in this context?
  3. Can we interpret a confidence interval as a probability statement about μ\mu?
  4. What does a confidence level mean in practical terms?
  5. 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.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

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