| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2018 |
| Session | Specimen |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Hypothesis test of Spearman’s rank correlation coefficien |
| Type | Hypothesis test for positive correlation |
| Difficulty | Standard +0.3 This is a straightforward application of the Spearman's rank correlation formula with clearly given rankings and a standard hypothesis test using critical values. The calculation involves finding differences, squaring them, and applying the formula—routine procedural work for S3 students with no conceptual challenges or novel problem-solving required. |
| Spec | 5.08e Spearman rank correlation5.08f Hypothesis test: Spearman rank |
| Rank | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| Judge 1 | \(S\) | \(N\) | \(B\) | \(C\) | \(T\) | \(A\) | \(Y\) | \(R\) | \(L\) |
| Judge 2 | \(S\) | \(T\) | \(N\) | \(B\) | \(C\) | \(Y\) | \(L\) | \(A\) | \(R\) |
2. Nine dancers, Adilzhan $( A )$, Bianca $( B )$, Chantelle $( C )$, Lee $( L )$, Nikki $( N )$, Ranjit $( R )$, Sergei $( S )$, Thuy $( T )$ and Yana $( Y )$, perform in a dancing competition.
Two judges rank each dancer according to how well they perform. The table below shows the rankings of each judge starting from the dancer with the strongest performance.
\begin{enumerate}[label=(\alph*)]
\item Calculate Spearman's rank correlation coefficient for these data.
\item Stating your hypotheses clearly, test at the 1\% level of significance, whether or not the two judges are generally in agreement.
\begin{center}
\begin{tabular}{ | c | c | c | c | c | c | c | c | c | c | }
\hline
Rank & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\
\hline
Judge 1 & $S$ & $N$ & $B$ & $C$ & $T$ & $A$ & $Y$ & $R$ & $L$ \\
\hline
Judge 2 & $S$ & $T$ & $N$ & $B$ & $C$ & $Y$ & $L$ & $A$ & $R$ \\
\hline
\end{tabular}
\end{center}
(a) Calculate Spearman's rank correlation coefficient for these data.
\end{enumerate}
\hfill \mbox{\textit{Edexcel S3 2018 Q2 [9]}}