| Exam Board | OCR MEI |
|---|---|
| Module | Further Statistics Major (Further Statistics Major) |
| Year | 2024 |
| Session | June |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Hypothesis test of Spearman’s rank correlation coefficien |
| Type | Hypothesis test for negative correlation |
| Difficulty | Standard +0.3 This is a straightforward application of Spearman's rank correlation test with clear structure: explain why Spearman's (recognizing non-linearity from scatter diagram), state random sampling requirement, then execute a standard hypothesis test with n=10. The calculation involves ranking 10 values and applying the formula—routine for Further Statistics students with no novel problem-solving required. |
| Spec | 5.08e Spearman rank correlation5.08f Hypothesis test: Spearman rank |
| Age | 22 | 29 | 36 | 39 | 53 | 57 | 60 | 71 | 76 | 82 |
| Grip strength | 38 | 46 | 42 | 49 | 37 | 47 | 36 | 33 | 34 | 24 |
| Answer | Marks | Guidance |
|---|---|---|
| 6 | (a) | Because the scatter diagram appears to be curvilinear rather |
| Answer | Marks |
|---|---|
| bivariate Normal. | M1 |
| Answer | Marks |
|---|---|
| [2] | 3.5a |
| 2.4 | For elliptical or curvilinear |
| Answer | Marks | Guidance |
|---|---|---|
| 6 | (b) | The sample must be random |
| [1] | 1.2 | Do not allow ‘Random on random’ |
| 6 | (c) | DR |
| Answer | Marks |
|---|---|
| Please annotate page 9 | B1 |
| Answer | Marks |
|---|---|
| [8] | 1.1 |
| Answer | Marks |
|---|---|
| 2.2b | For any ranking. |
| Answer | Marks | Guidance |
|---|---|---|
| For comparison provided | rs | < 1. (provided sensibly |
| obtained) Allow | 0.7212 | > |
| Answer | Marks | Guidance |
|---|---|---|
| Age | 1 | 2 |
| Grip | 6 | 8 |
Question 6:
6 | (a) | Because the scatter diagram appears to be curvilinear rather
than elliptical,
there is not enough evidence to suggest that the distribution is
bivariate Normal. | M1
A1
[2] | 3.5a
2.4 | For elliptical or curvilinear
For full answer (dependent on first mark)
Condone ‘not based on bivariate Normal’
Do not condone ‘the data is not bivariate Normal’
Do not condone ‘Normal bivariate’ rather than bivariate
Normal’
6 | (b) | The sample must be random | B1
[1] | 1.2 | Do not allow ‘Random on random’
6 | (c) | DR
Age 1 2 3 4 5 6 7 8 9 10
Grip 6 8 7 10 5 9 4 2 3 1
∑𝑑 2 = 284
Spearman’s rank coefficient = −0.7212
H : There is no association between age and grip strength in
0
the population
H : There is negative association between age and grip strength
1
in the population
For n = 10, 5% 1-tailed critical value is 0.5636
−0.7212 < −0.5636
Reject H . There is sufficient evidence to suggest that there is
0
negative association between age and grip strength (in the
population)
Please annotate page 9 | B1
B1
B1
B1
B1
B1
M1
A1
[8] | 1.1
1.1
1.1
3.3
2.5
3.4
1.1
2.2b | For any ranking.
Could rank in reverse order leading to +0.7212 and still get
full marks
BC
B0B0 for correlation Do not allow ρ unless defined
s
Need to see population in one or other of the hypotheses
in order to get two B1 marks
For comparison provided |rs| < 1. (provided sensibly
obtained) Allow |0.7212| > |0.5636|.
Dep on H negative association .
1
Must be in context.
Allow ‘We can assume that…’
Do not allow correlation. No marks for PMCC test
Age | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10
Grip | 6 | 8 | 7 | 10 | 5 | 9 | 4 | 2 | 3 | 16 A student is investigating the relationship between age and grip strength in adults. The student selects 10 people and records their ages in years and the grip strengths of their dominant hand, measured in kg. The data are shown in the table below, together with a scatter diagram to illustrate the data.
\begin{center}
\begin{tabular}{ | l | l | l | l | l | l | l | l | l | l | l | }
\hline
Age & 22 & 29 & 36 & 39 & 53 & 57 & 60 & 71 & 76 & 82 \\
\hline
Grip strength & 38 & 46 & 42 & 49 & 37 & 47 & 36 & 33 & 34 & 24 \\
\hline
\end{tabular}
\end{center}
\begin{center}
\includegraphics[max width=\textwidth, alt={}]{bab116b3-6e5f-44db-ac86-670e4040d649-05_634_1107_641_239}
\end{center}
The student decides to carry out a hypothesis test to investigate whether there is negative association between age and grip strength.
\begin{enumerate}[label=(\alph*)]
\item Explain why the student decides to carry out a test based on Spearman's rank correlation coefficient.
\item State what property of the sample is required in order for it to be valid to carry out a hypothesis test.
\item In this question you must show detailed reasoning.
Assuming that the property in part (b) holds, carry out the test at the $5 \%$ significance level.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Further Statistics Major 2024 Q6 [11]}}