OCR (non mei) S2 Wednesday 15th June 2016

Why must the answer for q2 be as a percentage?

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

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. Fantastic!

I got the same answers. Fantastic!

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?

how do you do question 2

how do you do question 2

predictions for grade boundaries? I thought it was quite a nice paper. What did other people think?

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.

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

Predictions for grade boundaries? I thought it was quite a nice paper. What did other people think?

71 - 100 ums
66 - a*
61 - a