What is a confidence interval?

What is a confidence interval?

• A. A single estimate of the population parameter.
• B. A range around a sample estimate within which the true population parameter lies with a given probability (e.g., 95%).
• C. The margin of error divided by sample size.
• D. The interval between the 2.5th and 97.5th percentile in data.

Answer: (B)

A confidence interval is a range around a sample estimate that expresses the uncertainty about the true population parameter. It reflects the idea that if we repeated the study many times, the method would produce intervals that contain the true parameter a specified proportion of the time, such as 95%. For example, if we estimate a population mean and compute a 95% confidence interval, we would say we are 95% confident that the true mean lies within that interval, given the method and assumptions used. It’s not about a probability that this exact interval contains the parameter for this one study; rather, it’s about the long-run performance of the estimation procedure. The other descriptions don’t capture this idea: a single point estimate is just the best estimate without an expressed range; a margin of error divided by sample size misstates how the interval is formed; and using data percentiles to define an interval does not necessarily reflect uncertainty about the population parameter in the confidence-interval sense.

A confidence interval is a range around a sample estimate that expresses the uncertainty about the true population parameter. It reflects the idea that if we repeated the study many times, the method would produce intervals that contain the true parameter a specified proportion of the time, such as 95%.

For example, if we estimate a population mean and compute a 95% confidence interval, we would say we are 95% confident that the true mean lies within that interval, given the method and assumptions used. It’s not about a probability that this exact interval contains the parameter for this one study; rather, it’s about the long-run performance of the estimation procedure.

The other descriptions don’t capture this idea: a single point estimate is just the best estimate without an expressed range; a margin of error divided by sample size misstates how the interval is formed; and using data percentiles to define an interval does not necessarily reflect uncertainty about the population parameter in the confidence-interval sense.