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 below. O A. We are 99% confident that the interval from 4.1 to 5.6 actually does contain the true value of u. B. It means that 99% of sample means fall between 4.1 and 5.6. C. There is a 99% chance that u will fall between 4.1 and 5.6. D. It means that 99% of all data values are between 4.1 and 5.6.

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### Question: Interpret a 99% Confidence Interval

**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 below:**

**A.** We are 99% confident that the interval from 4.1 to 5.6 actually does contain the true value of μ.

**B.** It means that 99% of sample means fall between 4.1 and 5.6.

**C.** There is a 99% chance that μ will fall between 4.1 and 5.6.

**D.** It means that 99% of all data values are between 4.1 and 5.6.

### Explanation:
A confidence interval is a range of values used to estimate the true value of a population parameter. In this case, we are estimating the true mean (μ) with 99% confidence. This means that if we were to take many samples and construct a confidence interval from each sample, approximately 99% of those intervals would contain the true mean μ.

### Correct Answer:
The correct interpretation of the 99% confidence interval is:

**A.** We are 99% confident that the interval from 4.1 to 5.6 actually does contain the true value of μ.

### Additional Clarifications:
- Option **B** is incorrect because the confidence interval pertains to the population parameter, not the proportion of sample means.
- Option **C** is incorrect because probabilities are not assigned to fixed parameters; the true mean μ is a fixed value.
- Option **D** is incorrect because the confidence interval does not directly describe the distribution of individual data values but the estimate of the population parameter.
Transcribed Image Text:### Question: Interpret a 99% Confidence Interval **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 below:** **A.** We are 99% confident that the interval from 4.1 to 5.6 actually does contain the true value of μ. **B.** It means that 99% of sample means fall between 4.1 and 5.6. **C.** There is a 99% chance that μ will fall between 4.1 and 5.6. **D.** It means that 99% of all data values are between 4.1 and 5.6. ### Explanation: A confidence interval is a range of values used to estimate the true value of a population parameter. In this case, we are estimating the true mean (μ) with 99% confidence. This means that if we were to take many samples and construct a confidence interval from each sample, approximately 99% of those intervals would contain the true mean μ. ### Correct Answer: The correct interpretation of the 99% confidence interval is: **A.** We are 99% confident that the interval from 4.1 to 5.6 actually does contain the true value of μ. ### Additional Clarifications: - Option **B** is incorrect because the confidence interval pertains to the population parameter, not the proportion of sample means. - Option **C** is incorrect because probabilities are not assigned to fixed parameters; the true mean μ is a fixed value. - Option **D** is incorrect because the confidence interval does not directly describe the distribution of individual data values but the estimate of the population parameter.
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