OCR (non mei) S2 Wednesday 15th June 2016

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?


Posted from TSR Mobile

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.

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.