I am fitting the following model to my data $y = \beta_0 + \beta_1 x_1 + \beta_2 x_2$ and the claim I want to be able to make is that $\beta_1 = 0$ and $\beta_2 \neq 0$. I am going to use bootstrapping for this purpose. However, I don't know how to set up a test statistic for my claim since I have $\beta_1 \neq 0$ in my null hypothesis.
On a higher level what I want to show is that my output $y$ is not affected by $x_1$ whereas the variable $x_2$ helps me predict this output.
My apologies in advance if my question is ill-posed or silly. I am still in the process of coming up with a precise formulation of my problem. So any constructive feedback is appreciated.