I am told to test the hypothesis and this is what I did:
$H_{0}:\beta_{1}=0$
$H_{a}:\beta_{1}\not=0$
So then I have $$t^{*}=\dfrac{\hat{\beta_{1}}-\beta_{1}}{\dfrac{s_{\beta_1}}{\sqrt n}}$$
$\beta_{1}$=.5 and $\hat{\beta_{1}}$=.283
n=10 and $s_{\beta_{1}}$=.26
So $t^{*}$ ended up being equal to -2.67
The degree's of freedom is $n-1=9$ and so $t_{1}$ at $\alpha=.05$ is 2.262
So since |$t^{*}$|>2.62, we can reject.
I am unsure if that is perfectly correct and it probably is not, and if that is the case can you explain why? Thanks.