What is a confidence interval?

What is a confidence interval?

• A. The range of values in which a specified probability of the means of repeated samples would be expected to fall.
• B. The probability that the population mean lies within a single sample's interval.
• C. The exact value of the population mean.
• D. The range that contains 95% of individual observations.

Answer: (A)

A confidence interval is a range of values calculated from the data that is believed, with a specified level of certainty (like 95%), to contain the population mean. If you repeated the study many times and computed an interval each time, a fixed proportion of those intervals would include the true mean. This emphasizes the long-run performance of the method and the precision of the estimate based on sample size and variability. This isn’t about the probability that the population mean lies in a single, specific interval from one study, and it isn’t the exact value of the population mean. It also isn’t the range that would contain 95% of individual observations—that would be a prediction interval for individual data points, not for the mean.

A confidence interval is a range of values calculated from the data that is believed, with a specified level of certainty (like 95%), to contain the population mean. If you repeated the study many times and computed an interval each time, a fixed proportion of those intervals would include the true mean. This emphasizes the long-run performance of the method and the precision of the estimate based on sample size and variability.

This isn’t about the probability that the population mean lies in a single, specific interval from one study, and it isn’t the exact value of the population mean. It also isn’t the range that would contain 95% of individual observations—that would be a prediction interval for individual data points, not for the mean.