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Exam Standards

L

leafy

Member
There was an article in the latest issue of 'The Actuary' on one of the questions in the CT exam on Statistical Models.
It showed the question set and the model answer required by the exam board and showed where the author of the article disagreed strongly with the ambiguity in the question from a Mathematical point of view. It mentioned 'Independant and Indentically distributed' twice in the question. The first time it meant Pair-wise, the second time it didn't.

Coming to the question directly from the notes and with no mathematical back-ground I can see how people were able to make the correct assumption as to what the Examiners had in mind. But having studied Mathematics as a degree the words have a more reigorous meaning to me (and the author of the article). Like him I would have got the question wrong simply because I would have assumed that the question was *not* ambiguous, and therefore its proper mathematical interpretation is the correct one.

It worried me that I could potentially be thwarted in an exam by having *more* rigorous understanding of Mathematics.
Is anything being done to prevent this situation occuring in the future, or are we supposed to treat every Mathematical statement in the exams in a 'looser' sense?

Thank you,
leafy
 
Following on from what I posted before, I came across this in ActEd's own notes that I think sums up what I was talking about perfectly.

If you have it to hand: Page 22 of Chapter 14, Analysis of Variance, for subject CT3, Probability and Mathematical Statistics.

I quote:
"Note that Core Reading carries out a two-sided test and this is what is expected in the exam. It would be natural to choose a one-sided test as we have arranged the means in increasing order, however, this is not the approach used."
Click to expand...

So what this is effectively saying is that the natural, and logical approach for any mathematician attempting this particular question is to use a one-tail test. However, for some reason that is not explained, in the exam we would be required to use a two-tailed test. So unless you specifically remember this case having a more advanced knowledge of mathematics actually counts against you!
I don't understand why the examiners are allowed to make up their own laws of mathematics.

If anyone else comes across situations like this could they please post them here so that no-one gets caught out by a situation such as this!

leafy
 
Hi there Leafy - well I put that comment in the notes because it didn't make sense to me why the Core Reading wouldn't do a one-sided test (as we previously sorted them into increasing order). So I put that in to at least let people they're not alone in thinking the 'obvious' way - and hopefully reduce errors.

But I have to wonder whether I am missing something (in a mathematical sense!)

Anyone?
 
No, I agree with you. (I'm a mathematician)

The test H0 was: mu2 = mu3.

Since the means are arranged in ascending order the alternative, and thus the H1, should be: mu2 < mu3.
This is because it is clear to see that mu2 <= mu3 in all situations.

No test is "wrong", but clearly allowing for a situation that we know to be impossible is foolish and redundant.
A one-sided test is the most appropriate to use for the exact reason that we have one-sided tests for situations like these.

Why must I forget everything that I know about mathematics to be able to correctly answer an Actuarial maths question?

leafy
 
Go on - make a difference!

leafy said:
Why must I forget everything that I know about mathematics to be able to correctly answer an Actuarial maths question?
Click to expand...

What I suggest is that you pass your comment directly to the Staff Actuary for CT3 - Sally Calder. She's a star - and I think she would value comments from you.
 
Go on make a difference!

leafy said:
Could you PM me a contact e-mail or similar?
Click to expand...

Should have received this now. Thanks for feeding back to the Profession - I believe it does make a difference.
 
I sent an email at the beginning of the week and am awaiting the reply.
I will post any reply I get here (as long as I get the permission of the person who replies to me) so that everyone can benefit.

leafy
 
Dear Leafy

I understand your concern having read the article and the examiners are
concerned about it too, mainly because of the effect it could have on
students.

Setting examinations is a rigorous process and the papers and solutions
are tested and checked several times. There may be instances when
questions could be interpreted differently and/or alternative solutions
are valid (as in the real world) which is why the examiners continue to
review the questions and solutions during the marking process. They take
into account any comments from the Staff Actuaries, the actuaries
marking the scripts and ActEd.

The solutions published in the examiners' reports are indicative of the
main points which the examiners expected but are not intended to
represent the only valid answers.

The overall aim of the examinations is to show your understanding and
application of the course material and ability to proceed to the next
stage in your career as an actuary. If you have any doubts as to how the
examiners might interpret something you do then a brief explanation
would help to demonstrate your understanding to them. For example, with
the one-sided vs two-sided test, a very brief comment supporting your
choice would be enough.

Regarding your concerns about the Core Reading material, this is
continually revised and we take into account feedback from Examiners,
Practise Boards and ActEd when updating the material to ensure that
there are no errors. If you have any specific concerns about the Core
Reading (the material reproduced in bold in your ActEd notes) then pass
them to your ActEd tutor who will contact us if there are any problems.

Regards

Trevor

Dr Trevor Watkins
Head of Education and CPD
The Actuarial Profession
Tel: +44 (0)1865 268234
Fax: +44 (0)1865 268244
www.actuaries.org.uk
Click to expand...

I think that covered most things actually...although the one/two-sided issue ball is apparently in ActEd's court...

leafy
 
Not entirely related, and I'm not sure if this is a Trevor Watkins thing or a Jane Curtis (as chair of it) thing, but the minutes of the last Student Consultative Committee are a lot duller than previous ones. In particular they don't list all the comments that came in, so you can't see any more if you were alone in commenting on something. I guess it also means that it's harder for people to follow up on comments that were made to see if anything happened...
 
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