Hi,
First, the hypothesis are not officially required for a McKinsey interview. That's smth Victor Cheng proposed to market his books. However, now there is a whole generation of interviewers who were prepared on his books and they might be looking for the hypothesis:)
There are two ways to use the hypothesis:
First - presenting a structure using the hypothesis. For example, if you are having a PE (private equity) case, you should do the following:
1) Make classic structure (market, company, competitors, feasibility of exit)
2) Make subpoints (e.g. in market: size, growth rates, profitability, segmentation, etc)
3) Present your 1st level Hypothesis:
4) Present the main 2nd level Hypothesis:
Another way is using the hypothesis to prioritize your analysis:
1) Make a structure: "Problem in sales may be related to Sales Motivation, Sales Strategy, Sales Coverage, and Sales Process:
2) Prioritize a part of the structure based on your knowledge / common sense / available data: "Taking into account that motivation is the core problem of the sales organization, I would like to prioritize this part of the analysis"
Good luck!
Hypothesis and frameworks are mostly just ways to you to keep track of where you are going and what you are working towards... and ensuring your interviewer knows how you think
Stating a hypothesis is good practice, but you really only want one after a little bit of time. Since some interviewers may request one earlier however (see Vlad's explanation on how it came about through Victor Cheng), you can do one as simple as "my hypothesis is that the client's objective is possible".
As for the framework question: you obviously need a framework, I don't think anyone would argue that. Where many candidates go wrong is in thinking that the "business", "4 Cs", "profitability" frameworks are enough. No matter what structure you chose - even a very standard & powerful framework -, you will need to adapt it to the problem at hand to make sure you are addressing the question. In a way, you can think of the framework as the base Harley Davidson. No self-respecting biker would leave it as is, everyone makes sure to personalize it. All the same, you want to personalize your framework to really cater to your client's question