Test Post

In this post we will see how many of the classical test statistics

\[z, t, F\]

come fritom viewing a random sample as defining a vector in space, and understanding the geometry of these vectors.

1 - Gaussian Vector

Let

\[X_1, \dots, X_n \sim N(\mu, \sigma^2)\]

be indepelendent and identically distributed random variables. Each such random sample can be viewed as a vector

\[(X_1, \dots, X_n) \in \mathbb{R}^n\]