Alternative hypothesis ($H_1$)

The alternative hypothesis specifies the parameter values or distributions against which a null hypothesis is tested. If the null is $\theta \in {\Theta }_0$, the alternative is $\theta \in {\Theta }_1$ with ${\Theta }_0\cap {\Theta }_1=\varnothing$. For example an upper one-sided comparison uses $\theta >{\theta }_0$, while a two-sided comparison uses $\theta \ne {\theta }_0$. The alternative determines the relevant rejection tail. A p-value is computed under the null; it is not the probability that the alternative is false.