Moderate -0.3 This is a standard one-tailed binomial hypothesis test with clearly stated hypotheses (p > 0.08), straightforward calculations, and routine interpretation. While it requires multiple steps (hypotheses, test statistic, critical value/p-value, conclusion), these are all procedural applications of AS-level statistics content with no conceptual challenges or novel problem-solving required.
The proportion of vegans in a city is thought to be 8%
The owner of an organic food café in this city believes that the proportion of their customers who are vegan is greater than 8%
To test this belief, a random sample of 50 customers at the café were interviewed and it was found that 7 of them were vegan.
Investigate, at the 5% level, whether this sample supports the owner's belief.
[5 marks]
Question 17:
17 | States both hypotheses using
correct notation.
If a letter other than p is used, it
must be correctly defined
Accept 8% for 0.08 | 2.5 | B1 | X is ‘Number of vegan customers
at the café’
H : p = 0.08
0
H : p > 0.08
1
Under H : X ~ B(50 , 0.08)
0
P(X ≥ 7) = 1 – P(X ≤ 6)
= 1 – 0.898128…
= 0.102
As 0.102 > 0.05
Do not reject H
0
There is insufficient evidence to
suggest that the proportion of
vegan customers at the café is
greater than 8%.
States model used
PI by
P(X ≥ 7) = 0.10
P(X ≥ 8) = 0.04
P(X ≤ 6) = 0.90
P(X ≤ 7) = 0.96
AWRT
Condone incorrect inequalities
Condone
P(X = 7) = 0.06
P(X = 8) = 0.03
AWRT as evidence of use | 1.1a | M1
Obtains 0.10
AWRT
Condone 0.04 for A1
AWRT
Or
Critical region reject H if X ≥ 8
0
OE | 1.1b | A1
Compares 0.102 AWRT to 0.05
and states H is not rejected.
0
Or
Compares 7 with critical region
and states H is not rejected.
0
Condone accept H and
0
Reject H
1
Must see clear comparison | 2.2b | A1
Concludes, from a fully correct
comparison, in context, by
referring to the proportion of
vegan customers being greater
than 8%
OE
Only award if B1 M1 A1 A1
Must not be too definite
e.g. Use of ‘insufficient’, ‘not
significant’, ‘not enough’ | 3.2a | R1
Question 17 Total | 5
Question Paper Total | 80
The proportion of vegans in a city is thought to be 8%
The owner of an organic food café in this city believes that the proportion of their customers who are vegan is greater than 8%
To test this belief, a random sample of 50 customers at the café were interviewed and it was found that 7 of them were vegan.
Investigate, at the 5% level, whether this sample supports the owner's belief.
[5 marks]
\hfill \mbox{\textit{AQA AS Paper 2 2024 Q17 [5]}}