Suppose we want to test if a coin is biased towards heads. We decide to toss the coin 10 times and record the number of heads.
Let $X$ denote the number of heads occurring in 10 independent tosses of the coin. and will carry out a hypothesis test with $X$ as the test statistic.
Let $H$ be the event that the coin lands on head, in a single toss. Set our hypothesis to be
$$H_0:P(H)=0.5$$ $$H_1:P(H)>0.5$$
Suppose in our execution of the $10$ tosses, we observe $4$ heads. This means $X=4$ is the test result we observe.
I believe the range of test results that are 'at least as extreme as the one observed' (in the context of finding the p-value) is $$4 \leq X \leq 10$$ as we are testing whether the coin is biased towards heads, thus requiring to us to find test results that have at least as many heads. Is this valid?