Confidence Interval (1 of 2)

A confidence interval is a range of values computed in such a way that it contains the estimated parameter a high proportion of the time. The 95% confidence interval is constructed so that 95% of such intervals will contain the parameter. Similarly, 99% of 99% confidence intervals contain the parameter. If the parameter being estimated were μ, the 95% confidence interval might look like the following:

12.5 ≤ μ ≤ 30.2

If other information about the value of the parameter is available, it should be taken into consideration when assessing the likelihood that the interval contains the parameter. As an extreme example, consider the case in which 1,000 studies estimating the value of μ in a certain population all resulted in estimates between 25 and 30. If one more study were conducted and if the 95% confidence interval on μ were computed (based on that one study) to be:

35 ≤ μ ≤ 45

then the probability that μ is between 35 and 45 is very low, the confidence interval not withstanding.

It is natural to interpret a 95% confidence interval on the mean as an interval with a 0.95 probability of containing the population mean. However, the proper interpretation is not that simple. As just discussed, one problem is that the computation of a confidence interval does not take into account any other information you might have about the value of the population mean.