Question 2:
2 | (a) | 0.401 (0.400863) | B2
[2] | 1.1
1.1 | Awrt 0.401. SC: If B0, give B1 for any two of 54.75, 173.4, 39.06 or
any two of 876, 2775, 625 seen, or for answer 0.4(00)
(b) | Points do not lie very close to a (straight) line | B1
[1] | 2.4 | OE, e.g. “moderately scattered” or “vaguely linear”. Must be in terms
of diagram, not e.g. “weak correlation”. Not “not very close together”,
not “weak gradient”, not just “positively correlated”. Ignore
comments about ellipses or bivariate normal. Allow sketch if
reasonably appropriate. No wrong extras, e.g. “through origin”.
(c) | H :  = 0, H :  > 0, where  is the population
0 1
pmcc between student’s height and dog’s height
or H : no correlation between dog owner’s
0
height and dog’s height, H : positive
1
correlation (B1 if “positive” omitted)
CV 0.4259 or p = 0.0619(32)
0.401 < 0.4259 or 0.062 > 0.05 so do not reject
H
0
Insufficient evidence that there is (positive)
correlation between student height and dog
shoulder height | B2
B1
M1ft
A1ft
[5] | 1.1
2.5
1.1
1.1
2.2b | Allow ρ defined in terms of either population or context (or both).
Allow H :   0. Allow r. Needs “coefficient” or “pmcc” oe
0
One error, e.g. two-tailed, or  not defined as above: B1.
H : taller dog owners do not have taller dogs, H : taller dog owners
0 1
have taller dogs: B1.
Allow “association”, allow “independent” (but needs 1-tail for B2)
Either, for p allow awrt 0.062. (Two-tailed CV 0.4973 is B0 here)
FT on their r if 0 < r < 1, and FT from 0.4973 but no other CV. Needs
like-with-like.
Contextualised, acknowledge uncertainty; not “there is evidence that
there is not positive correlation”. Don’t need “positive” here
(2-tailed test typically B1B0, B0, M1A1)
(d) | Different as shoulder height → weight not a
linear transformation, or “probably similar as
taller dogs weigh more”, etc | B1
[1] | 2.3 | “Yes”, “Different”, “not very different”, “little difference”, “similar”
but no stronger, or “unclear”, with reason based on a (positive)
relationship between height and weight of dogs; nothing completely
wrong seen.
Not “No”, “unlikely”, “probably not different”, “little to no
difference”, etc. Not relationship between owners and weights.
Their hypotheses | Comment | Mark
H : ρ = 0, H : ρ > 0, where ρ is the population pmcc
0 1 | Correct | B2
H : r = 0, H : r > 0, where r is the pmcc between heights of students and dogs
0 1 | Correct, allow r | B2
H : ρ = 0, H : ρ > 0, where  is the pmcc
0 1 | Both “population” and context omitted | B1
H : ρ = 0, H : ρ  0, where  is the pmcc
0 1 | Two errors | B0
H : no correlation between dog owner’s height and dog’s height, H : positive correlation
0 1 | Correct | B2
H : no correlation between dog owner’s height and dog’s height, H : there is correlation
0 1 | “Positive” omitted | B1
H : taller dog owners do not have taller dogs, H : taller dog owners have taller dogs
0 1 | As on MS | B1
H : dog owner’s height and dog’s height independent, H : not independent
0 1 | Allow this | B2
Their conclusion | Comments | Mark
Accept H . Insufficient evidence of correlation between heights
0 | Correct, allow “accept H ”.
0 | M1A1
There is insufficient evidence of correlation
[Condone omission of “do not reject H ”]
0 | No context. | M1A0
Do not reject H . There is significant evidence that there is no correlation between the heights
0 | Wrong | M1A0
Do not reject H . The mean reading age is 10.75 in this district
0 | Too assertive | M1A0
There is insufficient evidence to reject H . Taller students do not have taller dogs
0 | BOD | M1A1
Unlikely as this is linear coding | B0
Unlikely as weight is proportional to height | B0
No as taller dogs have greater weight | B0
Not likely to be different: weight is just as random as height | B0
Probably, because taller owners probably have heavier dogs | B0
Little to no difference as weight has some dependence on height,
so this is linear coding | B0
Probably be different, as heavier dogs need stronger owners | B0
Quite similar because height & weight are correlated | B1
Would be similar as tall dogs are heavier but hard to tell | B1
Weight proportional to height3 so PMCC would be larger | B1
Probably not very different as tall dogs weigh more | B1
Height & weight correlated so r similar but weaker | B1
Not much different as weight is often proportional to height | B1
Unclear as weight and height are correlated but hard to tell | B1
Question | Answer | Marks | AO | Guidance