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

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 $\mu$.

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

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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 $\mu$?
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.