In the context of confidence intervals, if Figure 7-7 shows 'line a' representing the range within which a population parameter is expected to fall with a certain level of confidence, what type of statistical forecasting does 'line a' most likely depict?

• A. A point estimate of the population mean $\mu$
• B. A confidence interval for the mean $\mu$
• C. A prediction interval for a single future observation
• D. A tolerance interval for a specified proportion of the population

Answer: (B)

Verified step by step guidance

1. Understand the concept of a point estimate: it is a single value used to estimate a population parameter, such as the sample mean \( \bar{x} \) estimating the population mean \( \mu \). This is represented by a single point, not a range.
2. Recall that a confidence interval provides a range of values within which the population parameter is expected to lie with a certain level of confidence (e.g., 95%). It is constructed around the point estimate and accounts for sampling variability.
3. Recognize that a prediction interval is different from a confidence interval because it predicts the range for a single future observation, which is generally wider due to additional variability.
4. Understand that a tolerance interval is designed to cover a specified proportion of the entire population with a certain confidence level, which is different from estimating the population mean.
5. Since 'line a' shows a range within which the population parameter is expected to fall with a certain confidence level, it most likely depicts a confidence interval for the mean.