For a given statistic calculated for a sample of observations (e.g., the mean), the confidence interval is a range of values around that statistic that are believed to contain, in a certain proportion of samples (e.g., 95%), the true value of that statistic.

For a given statistic calculated for a sample of observations (e.g., the mean), the confidence interval is a range of values around that statistic that are believed to contain, in a certain proportion of samples (e.g., 95%), the true value of that statistic.

• A. Confidence interval
• B. Cohen's d
• C. communality
• D. Complete separation

Answer: (A)

The idea being tested is how a confidence interval expresses our uncertainty about a population parameter after sampling. When you compute a statistic from a sample, like the mean, the confidence interval creates a range around that statistic. This range is constructed so that, if you repeated the study many times with fresh samples under the same conditions, a specified proportion of those intervals (for example, 95%) would contain the true population value of that statistic (the population mean, in this case). The level you choose (95%) determines how wide the interval tends to be: higher confidence means more width and more assurance that the interval captures the true value. The width depends on the standard error of the statistic and the critical value from the relevant distribution; larger samples give smaller standard errors and tighter intervals. In interpretation, you can say you are 95% confident that the interval contains the true mean based on the method used. It’s about the reliability of the estimation method across many samples, not a probability about this single interval. Other terms don’t describe this idea. Cohen's d is an effect size measuring the standardized difference between groups, not a range around a sample statistic. Communality relates to shared variance in factor analysis, not interval estimation. Complete separation is a situation in binary regression where a predictor perfectly separates outcomes, not about estimating a population parameter with a confidence interval.

The idea being tested is how a confidence interval expresses our uncertainty about a population parameter after sampling. When you compute a statistic from a sample, like the mean, the confidence interval creates a range around that statistic. This range is constructed so that, if you repeated the study many times with fresh samples under the same conditions, a specified proportion of those intervals (for example, 95%) would contain the true population value of that statistic (the population mean, in this case). The level you choose (95%) determines how wide the interval tends to be: higher confidence means more width and more assurance that the interval captures the true value. The width depends on the standard error of the statistic and the critical value from the relevant distribution; larger samples give smaller standard errors and tighter intervals.

In interpretation, you can say you are 95% confident that the interval contains the true mean based on the method used. It’s about the reliability of the estimation method across many samples, not a probability about this single interval.

Other terms don’t describe this idea. Cohen's d is an effect size measuring the standardized difference between groups, not a range around a sample statistic. Communality relates to shared variance in factor analysis, not interval estimation. Complete separation is a situation in binary regression where a predictor perfectly separates outcomes, not about estimating a population parameter with a confidence interval.