If a hypothesis is rejected at the $0.025$ level of significance, then it may be rejected or not rejected at the $0.01$ level. Is this statement true? If it is true can you explain it to me why? I cannot seem to understand why it would be true.
Also if it is any level more than $0.025$, should it be rejected?
On
I'm assuming when you say 'a hypothesis', you're referring to the alternative hypothesis and not the null hypothesis.
If we reject the alternative hypothesis at a value of $\alpha = 0.025$, then we can say that it will also be rejected at a value of $\alpha = 0.01$, as $0.01<0.025$ and, seeing that the condition for rejecting an alternative hypothesis is having a $p$ value greater than $\alpha$, we can definitely say that it will be rejected at a value of $0.01$. Does this make sense?
We can say for certain whether it would be rejected at a value of $\alpha > 0.025$, but we don't know what $\alpha$ value this would be.
If a claim is rejected at $0.01$ significance level, it will be rejected at $0.025$, but the other way around need not be true.