Which of the following calculations is not derived from the $confidence interval$?

• A. The $margin of error$
• B. The lower and upper bounds for the $population parameter$
• C. The $sample mean$
• D. The range of plausible values for the $population parameter$

Answer: (C)

Verified step by step guidance

1. Step 1: Understand what a confidence interval represents. A confidence interval provides a range of plausible values for a population parameter, typically constructed around a sample statistic such as the sample mean.
2. Step 2: Identify the components derived from the confidence interval. These include the margin of error, which quantifies the maximum expected difference between the sample statistic and the population parameter, and the lower and upper bounds, which define the interval itself.
3. Step 3: Recognize that the sample mean is the starting point or center of the confidence interval, not something derived from it. The confidence interval is calculated using the sample mean plus or minus the margin of error.
4. Step 4: Confirm that the range of plausible values for the population parameter is exactly what the confidence interval provides, as it shows where the true parameter is likely to lie with a certain level of confidence.
5. Step 5: Conclude that among the options, the sample mean is not derived from the confidence interval but rather used to construct it, while the other options are directly related to or derived from the confidence interval.