Which of the following best describes the main disadvantage of the moving average when used to estimate a population parameter in the context of confidence intervals?

• A. It always overestimates the true population mean.
• B. It requires knowledge of the population standard deviation $\sigma$.
• C. It can only be used for normally distributed data.
• D. It does not provide a measure of variability or uncertainty, making it difficult to construct a confidence interval.

Answer: (D)

Verified step by step guidance

1. Understand that a moving average is a technique used to smooth data by averaging subsets of observations, often to identify trends over time.
2. Recognize that while a moving average can provide an estimate of a central tendency (like a mean), it does not inherently provide information about the variability or spread of the data around that estimate.
3. Recall that constructing a confidence interval requires not only a point estimate (such as a mean) but also a measure of variability, typically the standard error, which reflects uncertainty in the estimate.
4. Note that the moving average alone does not give a standard error or any measure of uncertainty, so it cannot be directly used to form confidence intervals without additional calculations or assumptions.
5. Therefore, the main disadvantage of using a moving average to estimate a population parameter in the context of confidence intervals is that it lacks a measure of variability or uncertainty, which is essential for constructing confidence intervals.