Following on from yesterday’s PoSWW, here is a WitCH with plenty of words. It is again from the 2024 QLD Methods “Technology-free” Exam. The intended solution can be found in the marking guide (p 7), but I could not locate anything in the subject report on how students performed.
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I guess the selection into groups is random? Sine qua non?
That’s not the point, and you can assume that, but yeah they should say it.
I think they absolutely need to say the selection is random. Probably more so in this nonsense scenario they’ve created. As written I don’t think it would be entirely unreasonable for someone to think six random groups of 10 people were asked (presumably together and likely to support the same team) rather than six groups of 10 random people.
Unlike the previous post at least it’s clear to me though what’s expected. Even if, as already said, the whole scenario is stupid and there many and far better ways to ask a question that essentially boils down to a) make a column graph and b) what happens when you increase sample size.
I also take very minor issue with the marking for part a. Students are basically being asked to do five equal things that are marked unequally. Highly unlikely but worst case scenario some student (possibly rushing or distracted) accidently writes one of the 0.2 groups as 0.5 and has now lost 2 marks for one mistake.
As for the lack of comment in the subject report and I would hope that’s an indication that there were was nothing significant to say but they should to tell us that. Every question deserves at least some comment. Even if just a couple of sentences such as “90% of students got full marks. Errors were mostly due to carelessness.”
Why does it matter if the selection is random? You can graph data that was not randomly selected. (Although I admit I’m not sure what they are looking for in part b, beyond there being 101 possible values rather than just 11.)
EDIT: OK I looked at the marking guide, that is really dreadful. You have to assume not only that selection of groups is random, but that selection INTO the groups is random (which would strikes me as very odd given the story setup).
The second part, “describe the two ways ….” requires randomness in the selection, and maybe also independence of the samples. (These two properties seem to be often overlooked in phrasing stats. questions.) My assumption is that they are testing the idea that means of larger samples have smaller spread.
Part b is almost a POSWW.
Basically. But readers clearly get snowed by the illusion of depth.