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

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Why bother with a post grad? Are they even worth it? Have your say! 26-10-2016
1. For the last question I managed to put the type of error, the value of p(X>=20) and p(X>=19) and I claimed the probability of a type 2 would be the probability of p(x>=19) and didn't take it away from 1. How many method marks do youse think would be given? I was assuming 1 each for the boundary probabilities and 1 for the type of error but not entirely sure.
2. For 8 ii, we didn't have to run a complete test did we and state hypotheses etc? Just find out if it changed the result of the test?

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3. (Original post by GM16)
For 8 ii, we didn't have to run a complete test did we and state hypotheses etc? Just find out if it changed the result of the test?

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The question just says "Determine whether this makes a difference to theconclusion of the test" so you won't need to state the hypotheses again.
4. (Original post by marioman)
The question just says "Determine whether this makes a difference to theconclusion of the test" so you won't need to state the hypotheses again.
Phew, thanks

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5. (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 concur with all of these.
6. For 8ii I didn't calculate an unbiased variance. I followed through with just the number given and got the correct conclusion. How many marks will I lose out of 5?
7. (Original post by Mr M (jr))
I concur with all of these.
I keep thinking about my answer to 5ii) . . . . .

that the sample must be random for the significance test to be valid, and then going on to explain what a random sample is in this particular context. Xsanda's answer isn't the same. . . . . and so you don't concur with me. . . . .

To me the question is similar to question 6i) on the June 2014 paper...???????

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