| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2013 |
| Session | June |
| Marks | 8 |
| 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 two variables (7 data points), apply the formula, and compare to critical values at 5% significance. While it requires careful calculation and knowledge of the test procedure, it's a routine textbook exercise with no conceptual challenges or novel problem-solving required—slightly easier than average due to small sample size and direct application. |
| Spec | 5.08e Spearman rank correlation5.08f Hypothesis test: Spearman rank |
| University | \(A\) | \(B\) | \(C\) | \(D\) | \(E\) | \(F\) | \(G\) | |||
| 14.2 | 13.1 | 13.3 | 11.7 | 10.5 | 15.9 | 10.8 | |||
| 4.1 | 4.2 | 3.8 | 4.0 | 3.9 | 4.3 | 3.7 |
2. The table below shows the number of students per member of staff and the student satisfaction scores for 7 universities.
\begin{center}
\begin{tabular}{ | l | c | c | c | c | c | c | c | }
\hline
University & $A$ & $B$ & $C$ & $D$ & $E$ & $F$ & $G$ \\
\hline
\begin{tabular}{ l }
Number of \\
students per \\
member of staff \\
\end{tabular} & 14.2 & 13.1 & 13.3 & 11.7 & 10.5 & 15.9 & 10.8 \\
\hline
\begin{tabular}{ l }
Student \\
satisfaction \\
score \\
\end{tabular} & 4.1 & 4.2 & 3.8 & 4.0 & 3.9 & 4.3 & 3.7 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Calculate Spearman's rank correlation coefficient for these data.
\item Stating your hypotheses clearly test, at the $5 \%$ level of significance, whether or not there is evidence of a correlation between the number of students per member of staff and the student satisfaction score.
\end{enumerate}
\hfill \mbox{\textit{Edexcel S3 2013 Q2 [8]}}