Question 5:
5 | (a) | Bursts occur independently of one another ...
and at constant average rate or at a uniform rate | B1
B1
[2] | 3.3
3.3 | Allow “probabilities of bursts must be independent”.
Not “number in one interval independent of number in another.”
Not “constant probability”, not “constant rate”, not “average
constant rate”, not “mean  variance”.
B0B0 unless at least one contextualised.
Ignore “singly”, but otherwise if more than 2 given, max B1
(b) | These are not very close together
... so a Poisson distribution may not be valid
(Ignore “mean = variance for (exact) Poisson”) | M1
A1
[2] | 2.2b
1.2 | Comment on closeness (not on equality)
Inference, not too definite (i.e., not “not valid”).
“In Poisson they’re the same but here they’re different” M0
(c) | H : N has (follows) a Poisson distribution
0
H : N does not have a Poisson distribution
1 | B1
[1] | 1.1 | Allow H : “Poisson is a good model”, “data can be modelled by
0
…”, “data consistent with Poisson”, “data follows/fits Poisson”,
“supports”, but not “there is evidence that …” Not Poisson(3.55).
(d) | E (3) = 60P(3) = 12.85
f
(8 – 12.85)2/12.85
= 1.83(1207) | B1
M1
A1
[3] | 3.1a
1.1
1.1 | E in range [12.8, 12.9], can be inferred from answer
f
(8 – their E)2/their E needed if answer not correct
f f
Awrt 1.83
(e) | 9.202 < 9.488
Do not reject H .
0
There is insufficient evidence that the number
of bursts of song in 5-minute periods does not
have a Poisson distribution | B1
M1ft
A1ft
[3] | 1.1
1.1
2.2b | Compare their 9.202 with 9.488 (wrong 9.202 loses no marks)
Allow for comparison with 11.07 or 12.59, or, with reversed
conclusion, 7.815. FT on their 9.202
Contextualised or N, not too assertive, FT on their 9.202. Needs
double negative, not “can be modelled by …” etc.
Condone “Po(3.55)” here.
(f) | It affects the validity as it suggests that bursts
are not independent (as if one burst is heard it is
more likely that another will be) | B1
[1] | 3.2a | “Yes” or “less valid” or “not valid” oe, and reason in context.
Allow “bursts are not independent” or “not random” .
Not “N is not independent”, nor “not singly”.
Question | Answer | Marks | AO | Guidance