Edexcel S3 2013 June — Question 2 8 marks

Exam BoardEdexcel
ModuleS3 (Statistics 3)
Year2013
SessionJune
Marks8
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicHypothesis test of Spearman’s rank correlation coefficien
TypeHypothesis test for association
DifficultyStandard +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.
Spec5.08e Spearman rank correlation5.08f Hypothesis test: Spearman rank

2. The table below shows the number of students per member of staff and the student satisfaction scores for 7 universities.
University\(A\)\(B\)\(C\)\(D\)\(E\)\(F\)\(G\)
Number of
students per
member of staff
14.213.113.311.710.515.910.8
Student
satisfaction
score
4.14.23.84.03.94.33.7
  1. Calculate Spearman's rank correlation coefficient for these data.
  2. 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.

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]}}