Yeah that definition is good. For the purposes of understanding the definition, another way of looking at it is basically a 'statistical proof by contradiction

Yeah that definition is good. For the purposes of understanding the definition, another way of looking at it is basically a 'statistical proof by contradiction': 1. Assume null hypothesis is true 2. Compute test statistic 3. Ask the question, "What is the probability of obtaining that test statistic or one more extreme?" (this probability is the p-value) 4. Pick a threshold (usually 0.05 but this is totally arbitrary) 5. If p < threshold then conclude the null hypothesis is false and reject it. Reductio ad statistico absurdum.