Question 3:
3 | (i) | Because the scatter diagram does not suggest a
bivariate Normal distribution since it is does not
appear to be roughly elliptical (seems to possibly
have two ‘islands’) | E1
E1
[2] | 3.5a
3.5b | For not from bivariate Normal distn
For not elliptical | Do not accept ‘data is not
bivariate Normal’
Do not accept ‘Normal
bivariate’
(ii) | Rank x 1 2 3 4 5 6 7 8 9 10
Rank y 9 8 10 5 6 7 2 1 4 3
r = 0.818 (= – 9/11)
s | M1
A1
A1
[3] | 1.1a
1.1
1.1 | For using ranks
For correct ranks for y | Accept both reversed
Accept – 0.82, – 0.8182 or
better
(iii) | H : There is no association between level of
0
dissolved oxygen and amount of radium.
H : There is association between level of dissolved
1
oxygen and amount of radium.
For n = 10, 1% critical value = 0.7939
0.818 > 0.7939 so significant/Reject H .
0
The evidence suggests that there is some association
between level of dissolved oxygen and amount of
radium. | B1
B1
B1
M1
A1
[5] | 3.3
1.2
1.1
1.1
2.2b | B1 for H
0
B1 for H and population soi
1
Hypotheses must be in context (allow
hypotheses in terms of x & y)
NB H H NOT ito ρ
0 1
M1 for sensible comparison with
0.7939, leading to a conclusion,
provided |r| < 1
s
For non-assertive correct conclusion
in context and in terms of H . FT their
1
r
s | Hypotheses as shown in
answer column should be
understood to imply
population
No further marks from here
if wrong cv used.
See additional notes.
(iv) | The significance level is the probability of rejecting
the null hypothesis when in fact it is true.
e.g. If there is no association between x and y only
about 1 sample in 100 would lead to the conclusion
that there is an association between x and y. | E1
E1
[2] | 2.4
1.2 | For relating this to the context.
Rank x | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10
Rank y | 9 | 8 | 10 | 5 | 6 | 7 | 2 | 1 | 4 | 3