| Exam Board | OCR |
|---|---|
| Module | Further Statistics AS (Further Statistics AS) |
| Session | Specimen |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Hypothesis test of Spearman’s rank correlation coefficien |
| Type | Calculate and interpret coefficient |
| Difficulty | Moderate -0.8 This is a straightforward application of Spearman's rank correlation coefficient formula with clear tabulated data. Students need to rank both sets of scores, calculate differences, and apply the standard formula - all routine procedures for Further Statistics. The interpretation part requires only basic understanding of correlation. While it's a multi-step calculation, it involves no conceptual challenges or problem-solving beyond textbook methods. |
| Spec | 5.08e Spearman rank correlation |
| Concert | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| Score by critic \(P\) | 12 | 11 | 6 | 13 | 17 | 16 | 14 |
| Score by critic \(Q\) | 9 | 13 | 8 | 14 | 18 | 16 | 20 |
| Answer | Marks | Guidance |
|---|---|---|
| 1 | (i) | Rankings |
| Answer | Marks |
|---|---|
| 7(cid:117)48 7 | *M1 |
| Answer | Marks |
|---|---|
| [4] | 1.1a |
| Answer | Marks |
|---|---|
| 1.1 | Rank both, can be reverse order |
| Answer | Marks | Guidance |
|---|---|---|
| 1 | (ii) | Strong agreement/association in rankings/views |
| [1] | 2.2b | e |
| Answer | Marks | Guidance |
|---|---|---|
| 1 | 2 | 3 |
| 1 | 3 | 2 |
| Answer | Marks |
|---|---|
| 1(ii) | S |
Question 1:
1 | (i) | Rankings
1 2 3 4 5 6 7
1 3 2 4 7 5 6
(cid:166)d2 (cid:32)8
6(cid:117)8 6
r (cid:32)1(cid:16) (cid:32) or 0.857
s
7(cid:117)48 7 | *M1
A1
dep*M1
A1
[4] | 1.1a
1.1
1.1
1.1 | Rank both, can be reverse order
(cid:166)d2 (cid:32)8 BC
n
Use of correct formula
awrt 0.857
1 | (ii) | Strong agreement/association in rankings/views | B1
[1] | 2.2b | e
Not strong correlation/relationship
1 | 2 | 3 | 4 | 5 | 6 | 7
1 | 3 | 2 | 4 | 7 | 5 | 6
--- 1(i) ---
1(i)
n
e
m
i
c
e
p
--- 1(ii) ---
1(ii) | S
--- 1(iii) ---
1(iii)Two music critics, $P$ and $Q$, give scores to seven concerts as follows.
\begin{tabular}{|c|c|c|c|c|c|c|c|}
\hline
Concert & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\
\hline
Score by critic $P$ & 12 & 11 & 6 & 13 & 17 & 16 & 14 \\
\hline
Score by critic $Q$ & 9 & 13 & 8 & 14 & 18 & 16 & 20 \\
\hline
\end{tabular}
\begin{enumerate}[label=(\roman*)]
\item Calculate Spearman's rank correlation coefficient, $r_s$, for these scores. [4]
\item Without carrying out a hypothesis test, state what your answer tells you about the views of the two critics. [1]
\end{enumerate}
\hfill \mbox{\textit{OCR Further Statistics AS Q1 [5]}}