AQA Paper 3 2024 June — Question 19 9 marks

Exam BoardAQA
ModulePaper 3 (Paper 3)
Year2024
SessionJune
Marks9
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicHypothesis test of binomial distributions
TypeTwo-tailed test critical region
DifficultyStandard +0.3 This is a standard A-level hypothesis test for a binomial proportion with straightforward application of critical regions at 10% significance level. Part (b) requires finding critical values from tables (routine but multi-step), while parts (a), (c), and (d) test basic understanding of hypothesis testing and data set limitations. The question is slightly above average difficulty due to the two-tailed test and the need to work with cumulative probabilities, but remains a textbook-style statistics question with no novel problem-solving required.
Spec2.05b Hypothesis test for binomial proportion2.05c Significance levels: one-tail and two-tail
It is known that 80% of all diesel cars registered in 2017 had carbon monoxide (CO) emissions less than 0.3 g/km. Talat decides to investigate whether the proportion of diesel cars registered in 2022 with CO emissions less than 0.3 g/km has **changed**. Talat will carry out a hypothesis test at the 10% significance level on a random sample of 25 diesel cars registered in 2022.
    1. State suitable null and alternative hypotheses for Talat's test. [1 mark]
    2. Using a 10% level of significance, find the critical region for Talat's test. [5 marks]
    3. In his random sample, Talat finds 18 cars with CO emissions less than 0.3 g/km. State Talat's conclusion in context. [1 mark]
  2. Talat now wants to use his random sample of 25 diesel cars, registered in 2022, to investigate whether the proportion of diesel cars in England with CO emissions more than 0.5 g/km has changed from the proportion given by the Large Data Set. Using your knowledge of the Large Data Set, give **two** reasons why it is not possible for Talat to do this. [2 marks]
Question 19:
AnswerMarks
19(a)(i)States
H : p = 0.8
0
H : p ≠ 0.8
AnswerMarks Guidance
12.5 B1
0
H : p ≠ 0.8
1
AnswerMarks Guidance
Subtotal1
QMarking instructions AO
AnswerMarks
19(a)(ii)States or uses correct model
PI by calculation of one of
P(X  x) where x = [1, 24] or
P(X ≥ x) where x = [1, 25] or
P(X = x) where x = 0 or 25 or
by critical region of x  16 or
AnswerMarks Guidance
x ≥ 243.3 B1
P(X  15) = 0.0173 < 0.05
P(X  16) = 0.0468 < 0.05
P(X  17) = 0.1091 > 0.05
P(X ≥ 23) = 0.0982 > 0.05
P(X ≥ 24) = 0.0274 < 0.05
P(X ≥ 25) = 0.0038 < 0.05
Critical region is x  16, x ≥ 24
Obtains one of (List 1)
[0.017, 0.0174] or
[0.046, 0.047] or
[0.109, 0.11] or
[0.098, 0.0983] or
[0.027, 0.0274] or
[0.0037, 0.0038]
or
obtains one of (List 2)
[0.982, 0.983] or
[0.953, 0.954] or
[0.890, 0.891] or
[0.901, 0.902] or
[0.97, 0.973] or
[0.996, 0.9963]
PI by critical region of x  16 or
x ≥ 24
AnswerMarks Guidance
Ignore labels1.1a M1
Compares one probability from
List 1 with 0.05
or
compares one probability from
List 2 with 0.95
PI by critical region of x  16 or
AnswerMarks Guidance
x ≥ 241.1a M1
Obtains one of the critical
AnswerMarks Guidance
regions of x  16 or x ≥ 241.1b A1
Obtains both critical regions
x  16 , x ≥ 24
Accept critical region of x < 17
or 0  x < 17, x > 23
Condone use of any letter for x
or stating  16 or ≥ 24
AnswerMarks Guidance
throughout3.2a A1
Subtotal5
QMarking instructions AO
AnswerMarks
19(a)(iii)Concludes correctly in context
from a fully correct comparison
Conclusion must not be definite,
eg use of ‘suggest’, ‘support’ etc
Follow through the correct
comparison of 18 with their
critical region from part 19(a)(ii)
The comparison does not need
AnswerMarks Guidance
to be seen2.2b E1F
suggest that proportion of diesel
cars registered in 2022 with CO
emissions less than 0.3 g/km has
changed
AnswerMarks Guidance
Subtotal1
QMarking instructions AO
AnswerMarks
19(b)States one of the following
reasons
1. no diesel cars in the
LDS have CO
emissions more than
0.5 g/km
2. Values of CO emissions
for some diesel cars are
missing from LDS
3. LDS data is not
representative due to
only few regions in
England or some makes
AnswerMarks Guidance
of cars or only two years2.4 E1
emissions more than 0.5 g/km
The LDS only uses data from cars
in some regions in England but not
all
States a different reason
1. no diesel cars in the
LDS have CO
emissions more than
0.5 g/km
2. Values of CO emissions
for some diesel cars are
missing from LDS
3. LDS data is not
representative due to
only few regions in
England or some makes
AnswerMarks Guidance
of cars or only two years2.4 E1
Subtotal2
Question 19 Total9
Question Paper Total100 
Question 19:
--- 19(a)(i) ---
19(a)(i) | States
H : p = 0.8
0
H : p ≠ 0.8
1 | 2.5 | B1 | H : p = 0.8
0
H : p ≠ 0.8
1
Subtotal | 1
Q | Marking instructions | AO | Marks | Typical solution
--- 19(a)(ii) ---
19(a)(ii) | States or uses correct model
PI by calculation of one of
P(X  x) where x = [1, 24] or
P(X ≥ x) where x = [1, 25] or
P(X = x) where x = 0 or 25 or
by critical region of x  16 or
x ≥ 24 | 3.3 | B1 | X ⁓ B(25, 0.8)
P(X  15) = 0.0173 < 0.05
P(X  16) = 0.0468 < 0.05
P(X  17) = 0.1091 > 0.05
P(X ≥ 23) = 0.0982 > 0.05
P(X ≥ 24) = 0.0274 < 0.05
P(X ≥ 25) = 0.0038 < 0.05
Critical region is x  16, x ≥ 24
Obtains one of (List 1)
[0.017, 0.0174] or
[0.046, 0.047] or
[0.109, 0.11] or
[0.098, 0.0983] or
[0.027, 0.0274] or
[0.0037, 0.0038]
or
obtains one of (List 2)
[0.982, 0.983] or
[0.953, 0.954] or
[0.890, 0.891] or
[0.901, 0.902] or
[0.97, 0.973] or
[0.996, 0.9963]
PI by critical region of x  16 or
x ≥ 24
Ignore labels | 1.1a | M1
Compares one probability from
List 1 with 0.05
or
compares one probability from
List 2 with 0.95
PI by critical region of x  16 or
x ≥ 24 | 1.1a | M1
Obtains one of the critical
regions of x  16 or x ≥ 24 | 1.1b | A1
Obtains both critical regions
x  16 , x ≥ 24
Accept critical region of x < 17
or 0  x < 17, x > 23
Condone use of any letter for x
or stating  16 or ≥ 24
throughout | 3.2a | A1
Subtotal | 5
Q | Marking instructions | AO | Marks | Typical solution
--- 19(a)(iii) ---
19(a)(iii) | Concludes correctly in context
from a fully correct comparison
Conclusion must not be definite,
eg use of ‘suggest’, ‘support’ etc
Follow through the correct
comparison of 18 with their
critical region from part 19(a)(ii)
The comparison does not need
to be seen | 2.2b | E1F | There is insufficient evidence to
suggest that proportion of diesel
cars registered in 2022 with CO
emissions less than 0.3 g/km has
changed
Subtotal | 1
Q | Marking instructions | AO | Marks | Typical solution
--- 19(b) ---
19(b) | States one of the following
reasons
1. no diesel cars in the
LDS have CO
emissions more than
0.5 g/km
2. Values of CO emissions
for some diesel cars are
missing from LDS
3. LDS data is not
representative due to
only few regions in
England or some makes
of cars or only two years | 2.4 | E1 | No diesel cars in the LDS have CO
emissions more than 0.5 g/km
The LDS only uses data from cars
in some regions in England but not
all
States a different reason
1. no diesel cars in the
LDS have CO
emissions more than
0.5 g/km
2. Values of CO emissions
for some diesel cars are
missing from LDS
3. LDS data is not
representative due to
only few regions in
England or some makes
of cars or only two years | 2.4 | E1
Subtotal | 2
Question 19 Total | 9
Question Paper Total | 100
It is known that 80% of all diesel cars registered in 2017 had carbon monoxide (CO) emissions less than 0.3 g/km.

Talat decides to investigate whether the proportion of diesel cars registered in 2022 with CO emissions less than 0.3 g/km has **changed**.

Talat will carry out a hypothesis test at the 10% significance level on a random sample of 25 diesel cars registered in 2022.

\begin{enumerate}[label=(\alph*)]
\item \begin{enumerate}[label=(\roman*)]
\item State suitable null and alternative hypotheses for Talat's test.
[1 mark]

\item Using a 10% level of significance, find the critical region for Talat's test.
[5 marks]

\item In his random sample, Talat finds 18 cars with CO emissions less than 0.3 g/km.

State Talat's conclusion in context.
[1 mark]
\end{enumerate}

\item Talat now wants to use his random sample of 25 diesel cars, registered in 2022, to investigate whether the proportion of diesel cars in England with CO emissions more than 0.5 g/km has changed from the proportion given by the Large Data Set.

Using your knowledge of the Large Data Set, give **two** reasons why it is not possible for Talat to do this.
[2 marks]
\end{enumerate}

\hfill \mbox{\textit{AQA Paper 3 2024 Q19 [9]}}
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