if $P:=P_{H_0}$(To get an equally extreme outcomes that the observed), what does "equally extreme outcomes mean then? For an example in this situation. How does he get that " When saying extreme then you mean deviates more than |0.2| from 3.2 "
2026-03-26 14:17:10.1774534630
what does extreme really mean in P-value method
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If you have a normal distribution with mean $3.2$ and standard deviation $0.6$, it would be very surprising if the average of your observations turned out to be $8$. It would be less surprising if the average turned out to be $4$, so we would say that $8$ is more extreme than $4$. But $-10$ is more extreme than either because it is $13.2$ away from the mean rather than $0.8$ or $4.8$.
In general for a normal distribution, the further away from the mean, the more extreme (surprising) the result.
We want the p-value to be the probability of getting a result at least as extreme as that actually observed. Anything $\geq 3.4$ or $\leq 3.0$ is at least as far away from the expected mean (and hence at least as surprising/extreme) under the null hypothesis.