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# OCR (non mei) S2 Wednesday 15th June 2016

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1. (Original post by andygeor)
Why must the answer for q2 be as a percentage?
it asked for a percentage , it's one of those questions where you've gotta pay acute attention to the wording of the question .. . . . . . . . . . .not sure if you'd be penalised.
2. (Original post by JoshuaHope)
I did exactly the same thing! I'm just so annoyed cause it's worth so many. We should get about 3/14 I think for our original h0,h1 and then correct evaluation to your outcome
Yeah I'm so annoyed cuz it was soo stupid! Was it out of 13 or 14 was the central limit question out of 2?
I'm praying I've got enough for a B seeing as the rest of my answers match up but not too sure as grade boundaries will be high it was relatively easy
3. (Original post by xsanda)
Xsanda's solutions

1) Unbiased mean and variance of summarised data
E(V) = 268
Var(V) = 1912/13 = 147 [4]

2) Normal distribution, given P(M<1.00) = 5%
P(M>1.05) = 13.6% [6]

3) Approximated binomial
n large, np = 26 > 5, nq = 14 > 5
use normal distribution
P(X<=30) = 0.932 [7]

4) Poisson, P(X=4) = P(X=5)
λ = 5, P(X=5) = 0.175 [5]

5) School with 55% girls
i) P(G≥6) = 22% (above significance level), do not reject H₀ [7]
ii) Fixed prob of girl chosen, independent of previous Head Students [1]

6) Cars along a narrow road
i) Constant probability of cars throughout the minute, cars independent [2]
ii) λ = 6.5, P(4≤X<7) = 0.561[3]
iiia) N(30,30)
P(X>35) = 0.158 [6]
b) Not independent (narrow, slow road, so affected by car in front) [1]

7) Probability density function
i) x is a single sample value of X [1]
ii) a=1, b=1.5 [7]
iii) E(X) = 7/4 = 1.75 [3]

8) Animals dying at zoo
i) P(L<12.48) = 4.88% < 5%
reject H₀, substantial evidence zoos limit life expectancy [7]
ii) s² = 12.5
5.05% > 5%, do not reject H₀, insufficient evidence zoos limit life expectancy [5]
iii) yes, as the distribution of the original data is not given [1]

9) Poisson test, λ=11
i) reject if P(R≥20)
92% chance of Type II error [6]
I got the same answers, well with amendments from everyone else. Fantastic!
4. (Original post by WorkHardGoToUni)
I got the same answers. Fantastic!
Would you be able to explain 8ii??
5. (Original post by WorkHardGoToUni)
I got the same answers. Fantastic!
well done i think i lost 1 :P
6. I think it was a reasonably nice paper, there were more wordy questions about poisson etc than I would have liked though

Had a moment on the last question and found the critical region for R, stated it was a type II error as accept H0 given false, but then went on to calculate R>=20 instead of R<=19 so the ended up subtracting the correct answer from 1. Will this be 2/3 marks or so lost? And that should still be 95+ provided the rest are correct?
7. (Original post by olivia30)
I think it was a reasonably nice paper, there were more wordy questions about poisson etc than I would have liked though

Had a moment on the last question and found the critical region for R, stated it was a type II error as accept H0 given false, but then went on to calculate R>=20 instead of R<=19 so the ended up subtracting the correct answer from 1. Will this be 2/3 marks or so lost? And that should still be 95+ provided the rest are correct?
if all else is correct i'd imagine it's in the a* bracket (coming from a random person who just did this exam haha)
8. The question paper
Attachment 550499550501Attachment 550499550501
Attached Images

9. how do you do question 2
10. (Original post by arronpile)
how do you do question 2
Work out the value of sigma using standardising with phi^-1(0.05), use your zalue of sigma to work out z by standardising with the new value. P(Z>z)
11. (Original post by arronpile)
how do you do question 2
P(M<1.00)=0.05
P(Z<(1.00-1.03)/õ)=0.05
P(Z<0.03/õ)=0.95
0.03/õ=1.645
õ=0.03/1.645

Use that standard deviation to work out P(M>1.05)
P(Z>0.02/õ)=1-P(z<0.02/õ)=1-0.8637=0.1363
12. Either got 71 or 72/72. I put that the sample in 5ii which was the 8 head students, had to be drawn from a random sample, where each head student in the schools history had equal chance of being selected, because otherwise the result would be biased and hence incorrect
13. Predictions for grade boundaries? I thought it was quite a nice paper. What did other people think?
14. (Original post by workhardgotouni)
predictions for grade boundaries? I thought it was quite a nice paper. What did other people think?
71 - 100 ums
66 - a*
61 - a
15. (Original post by Mathematicus65)
Either got 71 or 72/72. I put that the sample in 5ii which was the 8 head students, had to be drawn from a random sample, where each head student in the schools history had equal chance of being selected, because otherwise the result would be biased and hence incorrect
Same here, you never know how strict they are going to be on wording.
16. so for Q8 I did part i in part ii and in part i I just did it without dividing by 50. Got the last part right, got the ho/1, any chance I'll get the marks for doing part i in ii? How many marks should I get over the Q??
17. (Original post by WorkHardGoToUni)
Same here, you never know how strict they are going to be on wording.
I am 99% sure that is correct. Because in the wording of the question it was hinting that you had to discuss the sample size of 8, hence why I mentioned random sampling ...
18. (Original post by XY123)
P(M<1.00)=0.05
P(Z<(1.00-1.03)/õ)=0.05
P(Z<0.03/õ)=0.95
0.03/õ=1.645
õ=0.03/1.645

Use that standard deviation to work out P(M>1.05)
P(Z>0.02/õ)=1-P(z<0.02/õ)=1-0.8637=0.1363
I got up to O~=0.03/1.645 how many marks out of 6 do you think I got
19. (Original post by WorkHardGoToUni)
Predictions for grade boundaries? I thought it was quite a nice paper. What did other people think?
The only bit that required some thinking was 7(ii) but it seems most got the answer. Probably high boundaries as per usual for S2.
20. (Original post by Mathematicus65)
71 - 100 ums
66 - a*
61 - a
Probably about right, the highest I've seen for an A* is 67, it was a very nice paper but I can't imagine the grade boundaries been higher than that.

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