| Exam Board | OCR |
|---|---|
| Module | FS1 AS (Further Statistics 1 AS) |
| Year | 2017 |
| Session | Specimen |
| Marks | 5 |
| Topic | Hypothesis test of Spearman’s rank correlation coefficien |
| Type | Calculate and interpret coefficient |
| Difficulty | Moderate -0.3 This is a straightforward application of Spearman's rank correlation coefficient formula requiring ranking two datasets and applying the standard formula. While it's a Further Maths topic (FS1), the calculation is mechanical with no conceptual challenges—just careful arithmetic. The interpretation in part (ii) is trivial. Slightly easier than average A-level difficulty due to its routine nature, though the ranking and calculation require care. |
| 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 |
Two music critics, $P$ and $Q$, give scores to seven concerts as follows.
\begin{center}
\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}
\end{center}
\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 FS1 AS 2017 Q1 [5]}}