The discussion centers on the method of inverting a test statistic to construct confidence intervals for the mean of a normal distribution with a known variance. Participants explore the potential for creating a new type of confidence interval that differs from traditional one-sided and two-sided intervals. The conversation highlights the need for clarity on the concept of pivotal intervals, which may be related to the construction of these new confidence intervals. The goal is to enhance understanding and application of this statistical method.
PREREQUISITESStatisticians, data analysts, and researchers interested in advanced statistical methods for constructing confidence intervals and enhancing their understanding of hypothesis testing.
A very powerful method of construction of a confidence interval/set for an unknown parameter, the mean of a normal distribution for example, is to invert a family of hypotheses tests about that parameter. This project is firstly to demonstrate the understanding of this method by using it to construct the usual one-sided and two-sided confidence intervals for the unknown mean of a normal distribution with a known variance. But the prize is given if a new confidence interval can be constructed by using this method for the unknown mean of a normal distribution with a known variance.
Here, `A new confidence interval' means a confidence interval that is
different from the usual one-sided and two-sided confidence intervals
for the unknown mean of a normal distribution with a known variance.