| Exam Board | AQA |
|---|---|
| Module | Paper 3 (Paper 3) |
| Session | Specimen |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Bivariate data |
| Type | Hypothesis test for correlation |
| Difficulty | Moderate -0.8 This is a straightforward correlation hypothesis testing question with mostly recall-based parts: stating standard hypotheses, comparing a test statistic to a critical value, recognizing that correlation coefficients must be between -1 and 1, and identifying that correlation doesn't imply causation. The only contextual knowledge required is familiarity with the Large Data Set. All parts are routine applications of basic statistical concepts with no problem-solving or novel insight required. |
| Spec | 5.08a Pearson correlation: calculate pmcc5.08d Hypothesis test: Pearson correlation |
| Sample size | Correlation coefficient | |
| A | 3827 | 0.088 |
| B | 3735 | 0.246 |
| C | 24 | 0.400 |
| D | 1250 | -1.183 |
| Answer | Marks |
|---|---|
| 10(a)(i) | Writes down correct |
| Answer | Marks | Guidance |
|---|---|---|
| written in words.) | AO2.5 | B1 |
| Answer | Marks |
|---|---|
| (a)(ii) | Compares 0.088 > 0.027 |
| Answer | Marks | Guidance |
|---|---|---|
| 0 | AO 3.1b | B1 |
| Answer | Marks |
|---|---|
| (b) | Explains that -1.183 is |
| Answer | Marks | Guidance |
|---|---|---|
| positive | AO 3.2b | E1 |
| Answer | Marks | Guidance |
|---|---|---|
| (c) | Explains that the masses | |
| removed are all zero | AO 2.4 | E1 |
| (d) | States one emission that |
| Answer | Marks | Guidance |
|---|---|---|
| hydrocarbons | AO 1.2 | B1 |
| (e) | Explains that Wesley is |
| Answer | Marks |
|---|---|
| significant.) | AO 2.4 |
| AO 2.2b | E1 |
| E1 | Wesley is saying that the bigger mass |
| Answer | Marks | Guidance |
|---|---|---|
| Total | 7 | |
| Q | Marking Instructions | AO |
Question 10:
--- 10(a)(i) ---
10(a)(i) | Writes down correct
hypotheses.
(Condone population
correlation coefficient
written in words.) | AO2.5 | B1 | H :ρ=0
0
H :ρ>0
1
(a)(ii) | Compares 0.088 > 0.027
and states yes (can
reject H )
0 | AO 3.1b | B1 | 0.088 > 0.027 so reject H
0
(b) | Explains that -1.183 is
outside the valid range
for the correlation
coefficient.
Do not accept that the
correlation should be
positive | AO 3.2b | E1 | The value of the correlation coefficient
must be between -1 and +1 so the
teacher asks her to remove the
calculation as -1.183 is outside this
range.
(c) | Explains that the masses
removed are all zero | AO 2.4 | E1 | They were zero.
(d) | States one emission that
Shona could use.
Accept particulates or
hydrocarbons | AO 1.2 | B1 | NOx
(e) | Explains that Wesley is
suggesting that greater
mass causes higher CO2
emissions, but this is not
necessarily true.
Infers either that the
sample size is too small
or the value of the
correlation coefficient
could be too small (to be
significant.) | AO 2.4
AO 2.2b | E1
E1 | Wesley is saying that the bigger mass
causes higher CO2 emissions, but we
only know that cars with a higher
mass tend to have higher emissions,
and the correlation may be due to
another factor.
It’s also only a small sample of 24 so
difficult to reach a conclusion.
Total | 7
Q | Marking Instructions | AO | Marks | Typical SolutionShona calculated four correlation coefficients using data from the Large Data Set.
In each case she calculated the correlation coefficient between the masses of the cars and the CO₂ emissions for varying sample sizes.
A summary of these calculations, labelled A to D, are listed in the table below.
\begin{tabular}{ccc}
& Sample size & Correlation coefficient \\
A & 3827 & 0.088 \\
B & 3735 & 0.246 \\
C & 24 & 0.400 \\
D & 1250 & -1.183
\end{tabular}
Shona would like to use calculation A to test whether there is evidence of positive correlation between mass and CO₂ emissions.
She finds the critical value for a one-tailed test at the 5% level for a sample of size 3827 is 0.027
\begin{enumerate}[label=(\alph*)]
\item
\begin{enumerate}[label=(\roman*)]
\item State appropriate hypotheses for Shona to use in her test. [1 mark]
\item Determine if there is sufficient evidence to reject the null hypothesis.
Fully justify your answer. [1 mark]
\end{enumerate}
\item Shona's teacher tells her to remove calculation D from the table as it is incorrect.
Explain how the teacher knew it was incorrect. [1 mark]
\item Before performing calculation B, Shona cleaned the data. She removed all cars from the Large Data Set that had incorrect masses.
Using your knowledge of the large data set, explain what was incorrect about the masses which were removed from the calculation. [1 mark]
\item Apart from CO2 and CO emissions, state one other type of emission that Shona could investigate using the Large Data Set. [1 mark]
\item Wesley claims that calculation C shows that a heavier car causes higher CO2 emissions.
Give two reasons why Wesley's claim may be incorrect. [2 marks]
\end{enumerate}
\hfill \mbox{\textit{AQA Paper 3 Q10 [7]}}