In statistics, which interval accounts for uncertainty in a single future observation rather than a population parameter?

In statistics, which interval accounts for uncertainty in a single future observation rather than a population parameter?

• A. Prediction interval
• B. Confidence interval
• C. Confidence band
• D. Tolerance interval

Answer: (A)

The concept being tested is predicting a single future observation. A prediction interval is designed to capture where a new individual value is likely to fall, not just what the population parameter (like the mean) is likely to be. It combines the uncertainty about the population mean with the random variation of an individual observation, so the interval is wider than a confidence interval for the mean alone. In practice, you estimate the mean with x̄ and the variability with s, and the prediction interval uses a form like x̄ ± t * s * sqrt(1 + 1/n) to reflect the extra source of variability from forecasting a new data point. Confidence intervals, by contrast, focus on the unknown parameter (the true mean) only, and confidence bands extend this idea across a range (often of x) rather than for a single future observation. Tolerance intervals aim to cover a specified proportion of the population with a given level of confidence. Thus, the interval that accounts for uncertainty in a single future observation is a prediction interval.

The concept being tested is predicting a single future observation. A prediction interval is designed to capture where a new individual value is likely to fall, not just what the population parameter (like the mean) is likely to be. It combines the uncertainty about the population mean with the random variation of an individual observation, so the interval is wider than a confidence interval for the mean alone. In practice, you estimate the mean with x̄ and the variability with s, and the prediction interval uses a form like x̄ ± t * s * sqrt(1 + 1/n) to reflect the extra source of variability from forecasting a new data point. Confidence intervals, by contrast, focus on the unknown parameter (the true mean) only, and confidence bands extend this idea across a range (often of x) rather than for a single future observation. Tolerance intervals aim to cover a specified proportion of the population with a given level of confidence. Thus, the interval that accounts for uncertainty in a single future observation is a prediction interval.