I was wondering why it is necessarily true that if a test statistic exceeds the critical value of t, then it will also be true that the p-value will not exceed the level of significance.

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#### Best Answer

I suppose this depends on what is meant by "exceed", but generally when people say a test statistics *exceeds* the critical value, they mean $|t|boldsymbol{>}t_{rm crit}$, and when they say the p-value *exceeds* the level of significance, they mean $pboldsymbol{<}alpha$. Thus, when the test statistic exceeds the critical value of t, the p-value *also* exceeds the level of significance.

As to why that fact is the case, it is simply because the value of $t_{rm crit}$ is *determined* by the point where $p<alpha$.

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