Question 6:
6 | (a) | Scatter diagram appears to be roughly elliptical
so the distribution may be bivariate Normal | E1
E1
[2] | 3.5a
2.4 | Condone ‘The data is bivariate normal’ or ‘The data comes
from a bivariate normal distribution’??
6 | (b) | DR
S =4713.62− 1 342.10273.65 [= 32.837]
xy 20
S = 5 9 8 9 .5 3 − 12  3 4 2 .1 0 2 [= 137.91]
x x 0
S = 3 9 1 9 .5 3 − 12  2 7 3 .6 5 2 [= 175.31]
y y 0
S 3 2 .8 3 7
r = x y =
S S 1 3 7 .9  1 1 7 5 .3 1
x x y y
= 0.211 | M1
M1
M1
A1
[4] | 1.1a
1.1
3.3
1.1 | For S
x y
For either S or S
x x yy
For general form including sq. root
Allow awrt 0.21 without incorrect working
6 | (c) | H :  = 0, H :  ≠ 0
0 1
where  is the population pmcc between x and y
For n = 20, the 5% critical value is 0.4438
Since 0.211 < 0.4438 the result is not significant, so there
is insufficient evidence to reject H
0
There is insufficient evidence at the 5% level to suggest
that there is correlation between download and upload
speed | B1
B1
B1
M1
A1
[5] | 3.3
2.5
3.4
1.1
2.2b | For both hypotheses Allow any symbol in place of ρ if
defined as population pmcc
For defining  NB Hypotheses in words only get B1 unless
population mentioned ‘between x and y’ may be seen in the
hypotheses alongside the correct hypotheses in symbols,
rather than in the definition of 
For correct critical value
For comparison and conclusion
Must be in context
FT their pmcc and cv (provided between -1 and +1) for M1
but not for A1
6 | (d) | Because download speed would not have a probability
distribution (so the distributional assumption could not be
met). | E[1]
[1] | 2.2a | Allow ‘the situation is not sampling from a bivariate
Normal population’ or ‘Statistical inference cannot be
carried out for non-random data’. Allow other suitable
answers.
E0 for ‘pmcc can only be found for random variables’