| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2003 |
| Session | June |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Hypothesis test of Spearman’s rank correlation coefficien |
| Type | Hypothesis test for association |
| Difficulty | Standard +0.3 This is a straightforward application of Spearman's rank correlation coefficient formula followed by a standard hypothesis test using critical value tables. The data is already ranked, requiring only calculation of differences, squaring, summing, and substituting into the formula. The hypothesis test is routine table lookup with n=8. Slightly above average difficulty due to being a two-part question requiring both calculation and interpretation, but involves no conceptual challenges or novel problem-solving. |
| Spec | 5.08e Spearman rank correlation5.08f Hypothesis test: Spearman rank |
| \backslashbox{Judge}{Skater} | (i) | (ii) | (iii) | (iv) | (v) | (vi) | (vii) | (viii) |
| A | 2 | 5 | 3 | 7 | 8 | 1 | 4 | 6 |
| B | 3 | 2 | 6 | 5 | 7 | 4 | 1 | 8 |
6. Two judges ranked 8 ice skaters in a competition according to the table below.
\begin{center}
\begin{tabular}{|l|l|l|l|l|l|l|l|l|}
\hline
\backslashbox{Judge}{Skater} & (i) & (ii) & (iii) & (iv) & (v) & (vi) & (vii) & (viii) \\
\hline
A & 2 & 5 & 3 & 7 & 8 & 1 & 4 & 6 \\
\hline
B & 3 & 2 & 6 & 5 & 7 & 4 & 1 & 8 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Evaluate Spearman's rank correlation coefficient between the ranks of the two judges.
\item Use a suitable test, at the $5 \%$ level of significance, to interpret this result.
\end{enumerate}
\hfill \mbox{\textit{Edexcel S3 2003 Q6 [11]}}