Hi Tutus,
This is fairly common in the BA world. Although I don't tend to ask for them myself (I'm a hiring BA Manager).
What they are looking for is that you:
1. Understand the full project lifecycle and where you fit into it.
2. Understand what skills and experience you have within that lifecycle
3. Understand what other peoples roles are in that lifecycle, including a broad idea of what their responsibilities are
4. See how comfortable you are in a presentation environment. BA's often have to give such presentations in the course of their duties, so this is a test of how comfortable you are with that.
5. How clear you are explaining a process to other people.
So overall, here are some tips.
a. Usually they give you a time limit - stick to it. If you know in advance how long that is, practice what you are going to say and time it. Don't go over that time. Also, make sure you leave some time to ask if they have any questions (this is a real plus point by the way - most people forget this). So if your time limit is 20 minutes say, speak for 15 mins, and then ask if there are any questions. They will have some. don't worry about it.
b. If you lose your train of thought, don't bumble on. Stop, ask yourself where you are and what is next in your presentation and then proceed. Don't forget to breath. It sounds silly but the number of times I have seen people charge through a presentation at 1 million miles an hour and then expect those listening to understand them is crazy.
c. If you can, have handouts to give, and go through them with your audience. It makes it easier to understand if they have something to follow in their hand.
d. If you are doing your presentation on a big screen or flip chart, don't be afraid to occasionally move about. Don't always move, it makes it hard to follow you, and thus follow hat you are saying. But, equally don't stand still like a statue.
e. Give both good and bad points of the project you were working on. For the bad points, don't say "John really messed it up" say how you handled the issue and resolved it. Remember though, they want to hear about you, not Dave from Testing. Its YOUR experience they want to know about.
f. They will ask you "why you didn't do this?", or "why didn't you do that?". Expect this and don't get put off your stride. Hindsight is a wonderful thing, but at the time you made a decision because it seemed the right thing to do. Always remember that you thought it was right at the time, but equally make sure you show your audience that you are not afraid to learn from your own experiences and from others. If they persist in querying why you did something, ask them (nicely) that you would be interested to know what they would have done and show real keenness to learn from their thoughts. They are basically trying to test if you are flexible or not. You want to show that you are.
g. If you are doing a PowerPoint presentation, or similar, don't make it just text. Make each page interesting to the audience and get them engaged where possible. Diagrams, graphs etc all help to keep peoples attention where you want it - on you and your presentation.
h. Lastly, be realistic. Don't say that you and you alone saved the world. Because lets face it, if you had, you wouldn't be applying for this job would you? They aren't expecting you to lead the project , but they want to see that you were a part of it. There is an important difference in that.
Good luck, and sorry I couldn't reply sooner. A little surprised in these days of Corona Virus that people are still having interviews!
Stewart