Inverting a test statistic is a powerful method for constructing confidence intervals for unknown parameters, particularly the mean of a normal distribution with known variance. The discussion focuses on demonstrating this method through the creation of standard one-sided and two-sided confidence intervals, as well as exploring the potential for developing a new type of confidence interval that differs from traditional approaches. Participants express a need for resources to better understand the concept, particularly regarding the "red" part of the method, with one suggesting it might relate to pivotal intervals. The conversation reflects a sense of urgency and frustration among users seeking clarity on the topic. Overall, the thread highlights the complexity of constructing innovative confidence intervals using hypothesis testing.