3.5 Interpretation of Confidence Intervals

Confidence intervals are inferential, not descriptive. That is, confidence intervals express a property of the population, not the sample. Furthermore, a confidence interval does NOT imply that there is 95% chance the population mean lies in the confidence interval. The analysis is complete: in this sample, the confidence interval will either cover the population mean or it will not.

If we repeated this same analysis on a number of samples, the confidence intervals generated by the analysis will cover the true population mean 95% of the time. Thus, in this particular instance, we do not know if the interval covers the mean, but we are 95% confident it will. The confidence interval is thus a statement about the estimation procedure and not about the specific interval generated in the sample.

Have a quick check of your understanding. Which of the following are correct?

  1. 95% of the 641 babies have a birthweight between 3079 and 3180 grams
  2. There is a 95% chance that the mean birthweight of all babies in the population is between 3079 and 3180 grams
  3. The confidence interval ranging from 3079 to 3180 grams would be expected to cover the true population proportion 95% of the time