This article relates lessons that are useful in the analysis of uncertainties in a complex measurement process, through a case study. It distinguishes between the settings for confidence intervals and those for prediction intervals. It illustrates testing of an assumed variance, shows how to separate the variance contributors in a calibration curve, discusses the use of independence of variance components, gives first-order approximations for combining random errors, and emphasizes the necessity of writing all the contributors to uncertainty in a single mathematical expression.