| Exam Board | OCR |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2010 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Hypothesis test of Spearman’s rank correlation coefficien |
| Type | Critical region or probability |
| Difficulty | Moderate -0.8 Part (i) requires recognizing perfect negative correlation without calculation (1 mark). Part (ii) is a routine application of Spearman's formula with n=3 (3 marks). Part (iii) involves basic probability - finding 1 favorable outcome among 3! = 6 possible permutations (3 marks). All parts are straightforward applications of S1 content with no problem-solving insight required, making this easier than average. |
| Spec | 5.01b Selection/arrangement: probability problems5.08e Spearman rank correlation |
| Skater | \(A\) | \(B\) | \(C\) |
| Judge \(P\) | 1 | 2 | 3 |
| Judge \(Q\) | 3 | 2 | 1 |
| Skater | \(A\) | \(B\) | \(C\) |
| Judge \(P\) | 1 | 2 | 3 |
| Judge \(R\) | 3 | 1 | 2 |
Three skaters, $A$, $B$ and $C$, are placed in rank order by four judges. Judge $P$ ranks skater $A$ in 1st place, skater $B$ in 2nd place and skater $C$ in 3rd place.
\begin{enumerate}[label=(\roman*)]
\item Without carrying out any calculation, state the value of Spearman's rank correlation coefficient for the following ranks. Give a reason for your answer. [1]
\begin{center}
\begin{tabular}{|c|c|c|c|}
\hline
Skater & $A$ & $B$ & $C$ \\
\hline
Judge $P$ & 1 & 2 & 3 \\
\hline
Judge $Q$ & 3 & 2 & 1 \\
\hline
\end{tabular}
\end{center}
\item Calculate the value of Spearman's rank correlation coefficient for the following ranks. [3]
\begin{center}
\begin{tabular}{|c|c|c|c|}
\hline
Skater & $A$ & $B$ & $C$ \\
\hline
Judge $P$ & 1 & 2 & 3 \\
\hline
Judge $R$ & 3 & 1 & 2 \\
\hline
\end{tabular}
\end{center}
\item Judge $S$ ranks the skaters at random. Find the probability that the value of Spearman's rank correlation coefficient between the ranks of judge $P$ and judge $S$ is 1. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR S1 2010 Q2 [7]}}