| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2020 |
| Session | October |
| Marks | 11 |
| 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 straightforward application of Spearman's rank correlation with standard hypothesis testing. Part (a) requires ranking data and applying the formula (routine calculation), part (b) is a standard one-tailed test comparing to critical values from tables, and part (c) tests understanding of tied ranks. All steps are procedural with no novel insight required, making it slightly easier than average. |
| Spec | 5.08e Spearman rank correlation5.08f Hypothesis test: Spearman rank |
| Athlete | \(A\) | \(B\) | \(C\) | \(D\) | \(E\) | \(F\) | \(G\) |
| 200 metre race (seconds) | 23.4 | 23.1 | 22.9 | 23.7 | 27.6 | 24.4 | 24.1 |
| Athlete | \(A\) | \(B\) | \(C\) | \(D\) | \(E\) | \(F\) | \(G\) |
| Long jump (metres) | 6.50 | 6.47 | 6.12 | 6.12 | 6.48 | 6.38 | 6.47 |
3. Each of 7 athletes competed in a 200 metre race and a 400 metre race.
The table shows the time, in seconds, taken by each athlete to complete the 200 metre race.
\begin{center}
\begin{tabular}{ | l | c | c | c | c | c | c | c | }
\hline
Athlete & $A$ & $B$ & $C$ & $D$ & $E$ & $F$ & $G$ \\
\hline
200 metre race (seconds) & 23.4 & 23.1 & 22.9 & 23.7 & 27.6 & 24.4 & 24.1 \\
\hline
\end{tabular}
\end{center}
The finishing order in the 400 metre race is shown below, with athlete $A$ finishing in the fastest time.\\
$\begin{array} { l l l l l l l } A & B & G & C & D & F & E \end{array}$
\begin{enumerate}[label=(\alph*)]
\item Calculate the Spearman's rank correlation coefficient between the finishing order in the 200 metre race and the finishing order in the 400 metre race.
\item Stating your hypotheses clearly, test whether or not there is evidence of a positive correlation between the finishing order in the 200 metre race and the finishing order in the 400 metre race. Use a $5 \%$ level of significance.
The 7 athletes also competed in a long jump competition with the following results.
\begin{center}
\begin{tabular}{ | l | c | c | c | c | c | c | c | }
\hline
Athlete & $A$ & $B$ & $C$ & $D$ & $E$ & $F$ & $G$ \\
\hline
Long jump (metres) & 6.50 & 6.47 & 6.12 & 6.12 & 6.48 & 6.38 & 6.47 \\
\hline
\end{tabular}
\end{center}
Yuliya wants to calculate the Spearman's rank correlation coefficient between the finishing order in the 200 metre race and the finishing order in the long jump for these athletes.
\item Without carrying out any further calculations, explain how Yuliya should do this.
\end{enumerate}
\hfill \mbox{\textit{Edexcel S3 2020 Q3 [11]}}