| Exam Board | OCR MEI |
|---|---|
| Module | Paper 2 (Paper 2) |
| Year | 2024 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Hypothesis test of Spearman’s rank correlation coefficien |
| Type | Compare with PMCC |
| Difficulty | Moderate -0.8 This is a straightforward hypothesis testing question requiring only interpretation of a given p-value (0.09195 > 0.05, so no evidence of association). Parts (a) and (b) involve basic scatter diagram interpretation. No calculations needed, just standard recall of hypothesis test procedure—easier than average A-level content. |
| Spec | 2.02c Scatter diagrams and regression lines2.02d Informal interpretation of correlation5.08d Hypothesis test: Pearson correlation |
| Answer | Marks | Guidance |
|---|---|---|
| Outlier correctly identified and circled on scatter diagram | B1 | AO 2.2b |
| Answer | Marks | Guidance |
|---|---|---|
| (weak) positive association or (weak) positive correlation | B1 | AO 1.1 |
| Answer | Marks | Guidance |
|---|---|---|
| \(0.09195\) correctly compared with \(0.05\) or \(0.025\) only | M1 | AO 3.4 |
| \(0.09195 > 0.025\) | A1 | AO 1.1 |
| insufficient evidence [at the 5% level] to suggest any association between cost of gas and cost of electricity isw | A1 | AO 2.2b |
## Question 11:
### Part (a):
Outlier correctly identified and circled on scatter diagram | B1 | AO 2.2b |
### Part (b):
(weak) positive association **or** (weak) positive correlation | B1 | AO 1.1 | allow e.g. as cost of electricity increases, cost of gas increases
### Part (c):
$0.09195$ correctly compared with $0.05$ or $0.025$ only | M1 | AO 3.4 | allow e.g. "$p$-value $> 0.05$"
$0.09195 > 0.025$ | A1 | AO 1.1 | allow $p$-value $> 0.025$
**insufficient evidence** [at the 5% level] to **suggest** any **association** between cost of gas and cost of electricity **isw** | A1 | AO 2.2b | A0 if refers to correlation rather than association; dependent on award of previous A1
---11 A householder is investigating whether there is any relationship between his monthly cost of gas and his monthly cost of electricity, both measured in pounds ( $\pounds$ ). The householder collects a random sample of monthly costs and presents them in the scatter diagram below.\\
\includegraphics[max width=\textwidth, alt={}, center]{8e48bbd3-2166-49e7-8906-833261f331ca-08_604_1452_392_244}
One of the points on the diagram represents the energy costs in a month when the householder was away on holiday for three weeks. The other points represent the energy costs in months when the householder did not go away on holiday.
\begin{enumerate}[label=(\alph*)]
\item On the copy of the diagram in the Printed Answer Booklet, circle the point which represents the month when the householder was most likely to have been away on holiday for three weeks.
\item With reference to the diagram, describe the relationship between the cost of gas and the cost of electricity.
The householder decides to test whether there is evidence to suggest that there is any association between the monthly cost of gas and the monthly cost of electricity. The value of Spearman's rank correlation coefficient for this sample is 0.4359 and the associated $p$-value is 0.09195 .
\item Determine whether there is any evidence to suggest, at the $5 \%$ level, that there is any association between the monthly cost of gas and the monthly cost of electricity.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Paper 2 2024 Q11 [5]}}