| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2015 |
| Session | June |
| 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 Spearman's rank correlation coefficient formula with clearly given rankings, followed by a standard hypothesis test using critical value tables. The calculation is mechanical (finding differences, squaring, summing) and the hypothesis test requires only stating H₀/H₁ and comparing to a critical value from tables. Slightly easier than average due to the routine nature and clear structure. |
| 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 | \(S\) | \(T\) | \(N\) | \(B\) | \(C\) | \(Y\) | \(L\) | \(A\) | \(R\) |
| Answer | Marks | Guidance |
|---|---|---|
| 2 | 46 | 51.69 |
Question 2:
2 | 46 | 51.69 | 46 | 51.69 | 0.6264 | 40.9364Nine 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{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}
\begin{enumerate}[label=(\alph*)]
\item Calculate Spearman's rank correlation coefficient for these data. [5]
\item Stating your hypotheses clearly, test at the 1\% level of significance, whether or not the two judges are generally in agreement. [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S3 2015 Q2 [9]}}