In statistics, the hypothesis testing is used for determining whether the null hypothesis can be rejected or failed to reject. For example, we use hypothesis testing in order determine the significance of the estimator in linear regression:
$H_0: \beta_1 = 0 \ \ \ H_1 : \beta_1 \neq 0$
My question is the approach of hypothesis testing in statistics related to intuitionist where the proof by contradiction is not permitted? Or to the classical reasoning?
Since, our main objective here is to show that $\beta_1$ is different from $0$, which means that the explanatory variable affects the dependent variable. In the above case we assumed that the parameter $\beta_1$ is equal to $0$. Thus, if we do not find enough proof that $\beta_1 = 0$, we reject the null hypothesis, which we conclude that $\beta_1 \neq 0$.