| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2016 |
| Session | June |
| Marks | 9 |
| 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 coefficient with standard hypothesis testing. Students must rank two variables, calculate the coefficient using the formula, and perform a one-tailed test at 5% significance. While it requires careful ranking and arithmetic, it follows a routine procedure with no conceptual challenges or novel insights—slightly easier than average due to its algorithmic nature. |
| Spec | 5.08e Spearman rank correlation5.08f Hypothesis test: Spearman rank |
| Salesperson | Distance travelled (in 1000's of km) | Commission earned (in \\(1000's) |
| A | 20.4 | 17.7 |
| B | 22.2 | 24.1 |
| C | 29.9 | 20.3 |
| D | 37.8 | 28.3 |
| E | 25.5 | 34.9 |
| \)F$ | 30.2 | 29.3 |
| G | 35.3 | 23.6 |
| H | 16.5 | 26.8 |
\begin{enumerate}
\item The table below shows the distance travelled by car and the amount of commission earned by each of 8 salespersons in 2015
\end{enumerate}
\begin{center}
\begin{tabular}{|l|l|l|}
\hline
Salesperson & Distance travelled (in 1000's of km) & Commission earned (in \$1000's) \\
\hline
A & 20.4 & 17.7 \\
\hline
B & 22.2 & 24.1 \\
\hline
C & 29.9 & 20.3 \\
\hline
D & 37.8 & 28.3 \\
\hline
E & 25.5 & 34.9 \\
\hline
$F$ & 30.2 & 29.3 \\
\hline
G & 35.3 & 23.6 \\
\hline
H & 16.5 & 26.8 \\
\hline
\end{tabular}
\end{center}
(a) Find Spearman's rank correlation coefficient for these data.\\
(b) Stating your hypotheses clearly, test, at the $5 \%$ level of significance, whether or not there is evidence of a positive correlation between the distance travelled by car and the amount of commission earned.\\
\hfill \mbox{\textit{Edexcel S3 2016 Q1 [9]}}