Which statement best describes a confidence interval for a mean in a report?

Which statement best describes a confidence interval for a mean in a report?

• A. The interval contains the true mean with a specified probability over repeated samples.
• B. The interval guarantees the true mean is within it for this sample.
• C. The interval equals the population mean.
• D. The interval is the same as the standard error.

Answer: (A)

Confidence intervals describe a range that would capture the true population mean in repeated samples a specified proportion of the time. So, a 95% interval means that if we repeated the study many times and calculated an interval each time, about 95% of those intervals would contain the true mean. For any single study, we can’t say the true mean definitely lies in this one interval—the population mean is fixed, and it either is inside or it isn’t. The interval is centered on the sample mean and widened by a margin of error that comes from the standard error and the chosen critical value; it is not the population mean itself, nor is it the standard error. The standard error measures precision, while the confidence interval uses that precision to form a range that, by the long-run method, would cover the true mean a specified proportion of the time.

Confidence intervals describe a range that would capture the true population mean in repeated samples a specified proportion of the time. So, a 95% interval means that if we repeated the study many times and calculated an interval each time, about 95% of those intervals would contain the true mean. For any single study, we can’t say the true mean definitely lies in this one interval—the population mean is fixed, and it either is inside or it isn’t. The interval is centered on the sample mean and widened by a margin of error that comes from the standard error and the chosen critical value; it is not the population mean itself, nor is it the standard error. The standard error measures precision, while the confidence interval uses that precision to form a range that, by the long-run method, would cover the true mean a specified proportion of the time.