An institution has offered a $1.6 million prize to anyone who can solve a famous maths problem that has puzzled mathematicians for more than a century.

Today our goal is to cover hypothesis testing and the basic z-test, as these are fundamental to understanding how the t-test works. We’ll return to the t-test soon — with real data.

In this paper we analyze implications of a singular contemporaneous disturbance covariance matrix for the estimation and hypothesis testing of systems of equations with autoregressive disturbances. We ...