A structure organizes the problem; a hypothesis tells the interviewer what you currently believe and what you want to test first.

You can have a clean issue tree and still work through it mechanically from left to right. Hypothesis-driven casing means using evidence to prioritize branches.

State an initial view based on the prompt, explain why it is plausible, and choose the first analysis that would confirm or reject it.

As new data arrives, update the hypothesis explicitly. The interviewer should be able to hear not only what you could analyze, but why you are choosing this next step now.

This is one of those things that makes more sense after a few live mocks than from reading about it.