confidence interval

A point estimate hands you a single number and stays silent about how much to trust it. A confidence interval instead hands you a range — 'the true value is somewhere around here, between this and that' — built so that the procedure is right a stated percentage of the time. It is the difference between saying 'the bridge will hold 50 tonnes' and saying 'the bridge will hold somewhere between 45 and 55 tonnes, and our method is reliable 95% of the time.' The range itself is the honest part.

A 95% confidence interval is typically the estimate plus or minus about two standard errors. The phrase '95% confidence' has a precise and often-misunderstood meaning: if you repeated the whole sampling-and-interval-building process many times, about 95% of the intervals produced would contain the true fixed parameter. For example, from a sample mean of 1,820 with a standard error of 30, a 95% interval is roughly 1,820 plus or minus 60, i.e. 1,760 to 1,880. A wider interval (say 99% confidence) is more likely to capture the truth but is less informative; more data narrows the interval at any fixed confidence level.

Actuaries use confidence intervals to communicate the uncertainty around reserves, mortality rates, and pricing factors honestly to managers and regulators. The discipline of reporting a range rather than a false-precise single number is central to professional standards. The crucial subtlety to keep straight: the true parameter is a fixed unknown, not random; it is the interval that is random. So a 95% interval does not mean 'there is a 95% probability the truth lies in this particular interval' — once computed, the truth either is or is not inside it. The 95% describes the long-run reliability of the method, not this one interval.