## 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?

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