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# AQA A2 Mathematics MS2B Statistics 2B - 21st June 2016

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1. *** AQA MS2B 21ST JUNE 2016 EXAM DISCUSSION THREAD ***

I can't seem to find a thread for this exam, so I thought it would be a good idea to start one up!

The purpose of this thread is to discuss any questions you may have about the MS2B unit. After the exam has taken place, we will hopefully be able to put an unofficial mark scheme together.

Date: 21st June 2016
Time: 9.00 am
Duration: 1h 30m

UNOFFICIAL MARK SCHEME
Here's the unofficial mark scheme for the MS2B paper. Unfortunately LaTex is playing up so I can't format some of the answers properly.

Question 1 (13 marks)

a) 0.703
b) 0.669
c) 0.133
d) 0.144
e) 0.622

Question 2 (4 marks)

Mean = 31.7 Variance = 2.96

Question 3 (13 marks)

a) P(X > 3) = 0.350
b) P (X < 3) and P (X > 3) = 0.315 (2 combinations)
c) Show E(X) = 3.08, Var(x) = 2.77
d) - Poisson distribution cannot have an upper limit
- Books not borrowed at a constant average rate
- Books may not be borrowed singly
- Mean does not equal variance
e) i) Mean = 30.8p
e) ii) Standard deviation = 16.7p (AWFW 16.6-16.7)

Question 4 (7 marks)

a) k = 10
b) P(X > 0.03) = 0.70
c) i) E(X) = 0.05
c) ii) Integrate, ans = 1/300
c) iii) SD(X) = 0.02895

Question 5 (13 marks)

a) Test statistic = 2.3386, CV = 2.706 so accept null
b) More diesel problems than expected - recommend petrol car

Question 6 (16 marks)

a) Test statistic = -2.20794, reject null
b) i) (14.9, 18.5)
b) ii) Claim not valid because 18.2 lies in CI
c) Claim not supported - sample mean on island C is greater than population mean

Question 7 (9 marks)

a) Draw probability density function
b) 73/24

Total: 75 marks

Credit to Suits101
2. Anyone taking this exam?
3. I'm taking this exam!

I have a quick question. When you're doing contingency table questions and you have to explain after you accept or reject the null hypothesis, is there a specific way to word it? In mark schemes it's different and they don't put "accept alternatively worded" next to it. So for example, for one question I accepted the null hypothesis (which Is correct) and I wrote "there is significant evidence at 10% level of significant to suggest that choice of subject is independent of gender" but the mark scheme wrote "there is insufficient evidence to suggest that choice of subject is associated with gender" which is what I said but just backwards. Are they picky on this? Is there a way to word this properly based on whether or not you reject null?

Also is it better to say "independent" or "no association"?? Or does it not matter?

Sorry this is long. Thanks in advance. And good luck to everyone!
4. (Original post by KB_97)
I'm taking this exam!

I have a quick question. When you're doing contingency table questions and you have to explain after you accept or reject the null hypothesis, is there a specific way to word it? In mark schemes it's different and they don't put "accept alternatively worded" next to it. So for example, for one question I accepted the null hypothesis (which Is correct) and I wrote "there is significant evidence at 10% level of significant to suggest that choice of subject is independent of gender" but the mark scheme wrote "there is insufficient evidence to suggest that choice of subject is associated with gender" which is what I said but just backwards. Are they picky on this? Is there a way to word this properly based on whether or not you reject null?

Also is it better to say "independent" or "no association"?? Or does it not matter?

Sorry this is long. Thanks in advance. And good luck to everyone!
Strictly speaking, we never 'accept' a null hypothesis (even though AQA mark schemes seem to allow this false statement). A contingency table/hypothesis test doesn't prove that a null hypothesis is true. When we carry out statistical tests, we assume that the null hypothesis is true unless there is sufficient evidence to suggest otherwise. In which case, we would 'reject Ho'. If there is insufficient evidence, we 'fail to reject Ho'. The amount of evidence required is determined by the significance level of the test.

It is incorrect to say "there is significant evidence at 10% level of significant to suggest that choice of subject is independent of gender" as this statement implies that you have strong evidence to accept the null hypothesis. As I briefly explained before, a hypothesis test provides/fails to provide evidence to reject a null hypothesis, it doesn't provide evidence to accept it.

In this example, there isn't enough evidence to reject Ho, so we cannot accept the alternative hypothesis. Putting this into context, "there is insufficient evidence to suggest that choice of subject is associated with gender". I hope you can now see why this statement isn't the same as your original answer.

With regards to your other question, I think it's fine to say 'independent' or 'no association' as these phrases mean the same thing.

The ideas behind statistical tests can be quite tricky to grasp at first but I hope that helps anyway!
5. (Original post by sam_97)
Strictly speaking, we never 'accept' a null hypothesis (even though AQA mark schemes seem to allow this false statement). A contingency table/hypothesis test doesn't prove that a null hypothesis is true. When we carry out statistical tests, we assume that the null hypothesis is true unless there is sufficient evidence to suggest otherwise. In which case, we would 'reject Ho'. If there is insufficient evidence, we 'fail to reject Ho'. The amount of evidence required is determined by the significance level of the test.

It is incorrect to say "there is significant evidence at 10% level of significant to suggest that choice of subject is independent of gender" as this statement implies that you have strong evidence to accept the null hypothesis. As I briefly explained before, a hypothesis test provides/fails to provide evidence to reject a null hypothesis, it doesn't provide evidence to accept it.

In this example, there isn't enough evidence to reject Ho, so we cannot accept the alternative hypothesis. Putting this into context, "there is insufficient evidence to suggest that choice of subject is associated with gender". I hope you can now see why this statement isn't the same as your original answer.

With regards to your other question, I think it's fine to say 'independent' or 'no association' as these phrases mean the same thing.

The ideas behind statistical tests can be quite tricky to grasp at first but I hope that helps anyway!
Thanks!! It makes more sense now.
6. (Original post by KB_97)
Thanks!! It makes more sense now.
No problem!
7. There doesn't seem to be many taking it, hahaha. Maybe it's just too early. Anyway, I'm taking it too. Are you ready for it?
8. (Original post by student0042)
There doesn't seem to be many taking it, hahaha. Maybe it's just too early. Anyway, I'm taking it too. Are you ready for it?
Heyya, I'm taking it!
I'm kind of ready, I think, depends on the style of questions, how about you ?
9. (Original post by Roxanne18)
Heyya, I'm taking it!
I'm kind of ready, I think, depends on the style of questions, how about you ?
Yeah, i'm the same, I think I'm ready. The last question on the paper last year was the differentiator, but by playing on my calculator I got the answer. Hopefully there will be no 'strange' questions this year, but if there are, I hope I'll be able to work out the answers by luck.
10. (Original post by student0042)
Yeah, i'm the same, I think I'm ready. The last question on the paper last year was the differentiator, but by playing on my calculator I got the answer. Hopefully there will be no 'strange' questions this year, but if there are, I hope I'll be able to work out the answers by luck.
I know, that question confused me so much! Hoping there wont be a similar one, really don't think I'd cope :/
Knowing how AQA have been so far I'm expecting there to be some strange questions unfortunately
Good luck to you!!
11. (Original post by Roxanne18)
I know, that question confused me so much! Hoping there wont be a similar one, really don't think I'd cope :/
Knowing how AQA have been so far I'm expecting there to be some strange questions unfortunately
Good luck to you!!
Are you in your second year? Our school does full A-level maths the first year and then full A-level further maths the second. So, I don't know if you've done either FP3 or M3, but they weren't anything like usual. M3 was absolutely dreadful.
12. (Original post by student0042)
Are you in your second year? Our school does full A-level maths the first year and then full A-level further maths the second. So, I don't know if you've done either FP3 or M3, but they weren't anything like usual. M3 was absolutely dreadful.
Yes final year. My school does the same as yours, so only doing Further this year.I did Fp3 and that was no where near what I was expecting. Sorry to hear about M3, I'm not doing that one, I'm doing fp1-4 M2 and S2
13. (Original post by Roxanne18)
Yes final year. My school does the same as yours, so only doing Further this year.I did Fp3 and that was no where near what I was expecting. Sorry to hear about M3, I'm not doing that one, I'm doing fp1-4 M2 and S2
I'm just doing all the further modules (except FP1 because I did it last year). At least FP4 was a normal paper.
14. (Original post by student0042)
I'm just doing all the further modules (except FP1 because I did it last year). At least FP4 was a normal paper.
Haha doesn't givve me much hope, I didn't like the middle of the fp4 paper :/ Though I never liked FP4!
Really hoping for a nice FP1 and S2 to bring up my FP3 and FP4 papers
15. (Original post by Roxanne18)
Haha doesn't givve me much hope, I didn't like the middle of the fp4 paper :/ Though I never liked FP4!
Really hoping for a nice FP1 and S2 to bring up my FP3 and FP4 papers
Knowing AQA, they'll make it difficult to make us cry in our exams. I don't think S2 should be that bad, but I said that about M3 haha
16. (Original post by Roxanne18)
Haha doesn't givve me much hope, I didn't like the middle of the fp4 paper :/ Though I never liked FP4!Really hoping for a nice FP1 and S2 to bring up my FP3 and FP4 papers
Well anyway, good luck! We've got plenty of time to nail down S2.
17. (Original post by student0042)
There doesn't seem to be many taking it, hahaha. Maybe it's just too early. Anyway, I'm taking it too. Are you ready for it?
I think I'm ready for it, just hope there's nothing too out of the ordinary in the exam.
18. (Original post by sam_97)
I think I'm ready for it, just hope there's nothing too out of the ordinary in the exam.
Hopefully there won't be. I don't know if you've sat any other maths exams already, but they've not been nice in half the ones I've taken, so you never know.
19. (Original post by student0042)
Hopefully there won't be. I don't know if you've sat any other maths exams already, but they've not been nice in half the ones I've taken, so you never know.
The only maths exam I have taken so far is FP3. I thought it was quite unusual at the time so I have a feeling that the other maths exams will follow the same pattern.
20. (Original post by sam_97)
The only maths exam I have taken so far is FP3. I thought it was quite unusual at the time so I have a feeling that the other maths exams will follow the same pattern.
I've taken that one and M3. I thought FP3 was strange but I could still manage it, but M3 was just much harder than usual. So, I'll have to be prepared for whatever they throw at us.

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