What does a 95% confidence interval mean?

What does a 95% confidence interval mean?

• A. We are 95% confident that these limits contain the actual mean of the population.
• B. There is a 95% probability that the sample mean equals the population mean.
• C. 95% of data fall within the interval.
• D. The population mean is within the interval in 95% of samples.

Answer: (A)

A 95% confidence interval expresses how often the method would capture the true population mean if you repeated the study many times. In other words, the interval is constructed so that, in the long run, about 95% of such intervals would contain the actual population mean. It does not mean there’s a 95% probability that this specific interval contains the mean, since the mean is fixed and the randomness is in the data and the interval you calculate. So the best interpretation is that we are 95% confident that these limits include the true mean. The other statements either misstate what the interval reflects (the relationship between the sample mean and population mean) or mix up concepts about data spread and repeated samples.

A 95% confidence interval expresses how often the method would capture the true population mean if you repeated the study many times. In other words, the interval is constructed so that, in the long run, about 95% of such intervals would contain the actual population mean. It does not mean there’s a 95% probability that this specific interval contains the mean, since the mean is fixed and the randomness is in the data and the interval you calculate.

So the best interpretation is that we are 95% confident that these limits include the true mean. The other statements either misstate what the interval reflects (the relationship between the sample mean and population mean) or mix up concepts about data spread and repeated samples.