Consider a person who claims to have favorable chances in a game in the sense that if you randomly draw one card from a set with as many red as black cards, said person has probability 0.6 of naming the correct color of the card instead of probability 0.5. To test this person's claim we have him guess 25 consecutive times, where the drawn card is put back in the set every time. We choose to believe him if he guesses correctly at least 17 times; otherwise we choose not to believe him.
I've made an attempt at defining suitable null and alternative hypotheses for this test along with a suitable critical region where $T = X$ is the test statistic. I've considered $p \leq 0.5$ and $p > 0.5$ as the null and alternative hypothesis respectively, which corresponds to the critical region $\{17, 18, \dots, 25\}$. But I'm not sure whether this is correct, as I'm still confused on what the hypotheses should look like given the context. Perhaps we would want to disprove the person's claim?
Would someone be so kind as to provide me with a hint to what the null and alternative hypothesis should look like, or whether what I've proposed is correct. Thanks in advance.