| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2011 |
| Session | June |
| Marks | 10 |
| 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 standard textbook application of Spearman's rank correlation coefficient with straightforward ranking (no ties), calculation using the formula, and a routine hypothesis test using critical value tables. The question requires multiple steps but follows a completely standard procedure with no novel insight or problem-solving required, making it slightly easier than average. |
| Spec | 5.08e Spearman rank correlation5.08f Hypothesis test: Spearman rank |
| Town | \(A\) | \(B\) | \(C\) | \(D\) | \(E\) | \(F\) | \(G\) |
| \(h\) | 14 | 20 | 16 | 18 | 37 | 19 | 24 |
| \(c\) | 52 | 45 | 43 | 42 | 61 | 82 | 55 |
A county councillor is investigating the level of hardship, $h$, of a town and the number of calls per 100 people to the emergency services, $c$. He collects data for 7 randomly selected towns in the county. The results are shown in the table below.
\begin{tabular}{|c|c|c|c|c|c|c|c|}
\hline
Town & $A$ & $B$ & $C$ & $D$ & $E$ & $F$ & $G$ \\
\hline
$h$ & 14 & 20 & 16 & 18 & 37 & 19 & 24 \\
\hline
$c$ & 52 & 45 & 43 & 42 & 61 & 82 & 55 \\
\hline
\end{tabular}
\begin{enumerate}[label=(\alph*)]
\item Calculate the Spearman's rank correlation coefficient between $h$ and $c$.
[6]
\item Test, at the 5\% level of significance, the councillor's claim. State your hypotheses clearly.
[4]
\end{enumerate}
After collecting the data, the councillor thinks there is no correlation between hardship and the number of calls to the emergency services.
\hfill \mbox{\textit{Edexcel S3 2011 Q2 [10]}}