What does the 95% confidence interval imply about the population mean?

What does the 95% confidence interval imply about the population mean?

• A. There is a 95% probability that the population mean lies within the interval.
• B. We are 95% confident that the population mean lies within the interval.
• C. We are 95% confident that these limits contain the actual mean of the population.
• D. The interval contains the population mean with 95% probability in all samples.

Answer: (C)

A 95% confidence interval expresses how often the method would capture the true population mean if you repeated the study many times. The best statement is that we are 95% confident these limits contain the actual mean of the population. Since the population mean is a fixed value, probability doesn’t apply to this single interval being true or false. Instead, the confidence level reflects the long-run success of the procedure: about 95% of the intervals produced from repeated samples would contain the true mean. The other options mix up probability with the fixed parameter or with every possible sample—these nuances make them misleading precisely in how confidence is interpreted.

A 95% confidence interval expresses how often the method would capture the true population mean if you repeated the study many times. The best statement is that we are 95% confident these limits contain the actual mean of the population. Since the population mean is a fixed value, probability doesn’t apply to this single interval being true or false. Instead, the confidence level reflects the long-run success of the procedure: about 95% of the intervals produced from repeated samples would contain the true mean. The other options mix up probability with the fixed parameter or with every possible sample—these nuances make them misleading precisely in how confidence is interpreted.