\(X_1,X_2,\dots,X_n\) denotes random sample following the model \[ X_i = \theta + e_i, \] random errors \(e_i\) are independently and identically distributed with a continuous probability density function \(f(t)\) symmetric around \(0\).

Hypothesis testing: \[ H_0: \theta = 0 \text{ versus } H_A: \theta > 0 \]

- A
*null hypothesis*is associated with a**contradiction**to a theory one would like to prove An

*alternative hypothesis*is associated with the actual theory one would like to prove