| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2006 |
| Session | January |
| Marks | 12 |
| 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 with standard hypothesis testing. Students must rank data, apply the formula (or use differences), and compare to critical values. While it requires multiple steps, each is routine for S3 level with no novel insight needed—slightly easier than average A-level questions overall. |
| Spec | 5.08e Spearman rank correlation5.08f Hypothesis test: Spearman rank |
| Age group (years) | 20-29 | 30-39 | 40-49 | 50-59 | 60-69 | 70 and over |
| Deaths from pneumoconiosis (1000s) | 12.5 | 5.9 | 18.5 | 19.4 | 31.2 | 31.0 |
| Deaths from lung cancer (1000s) | 3.7 | 9.0 | 10.2 | 19.0 | 13.0 | 18.0 |
7. The numbers of deaths from pneumoconiosis and lung cancer in a developing country are given in the table.
\begin{center}
\begin{tabular}{|l|l|l|l|l|l|l|}
\hline
Age group (years) & 20-29 & 30-39 & 40-49 & 50-59 & 60-69 & 70 and over \\
\hline
Deaths from pneumoconiosis (1000s) & 12.5 & 5.9 & 18.5 & 19.4 & 31.2 & 31.0 \\
\hline
Deaths from lung cancer (1000s) & 3.7 & 9.0 & 10.2 & 19.0 & 13.0 & 18.0 \\
\hline
\end{tabular}
\end{center}
The correlation between the number of deaths in the different age groups for each disease is to be investigated.
\begin{enumerate}[label=(\alph*)]
\item Give one reason why Spearman's rank correlation coefficient should be used.
\item Calculate Spearman's rank correlation coefficient for these data.
\item Use a suitable test, at the $5 \%$ significance level, to interpret your result. State your hypotheses clearly.\\
(5)
\end{enumerate}
\hfill \mbox{\textit{Edexcel S3 2006 Q7 [12]}}