| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2018 |
| Session | June |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Hypothesis test of Spearman’s rank correlation coefficien |
| Type | Hypothesis test for negative correlation |
| Difficulty | Standard +0.3 This is a standard S3 hypothesis testing question requiring ranking data, calculating Spearman's coefficient using the formula, and performing two routine significance tests with critical value lookups. While it has multiple parts and requires careful arithmetic, it follows a completely standard template with no novel problem-solving or conceptual challenges beyond textbook procedures. |
| Spec | 5.08a Pearson correlation: calculate pmcc5.08d Hypothesis test: Pearson correlation5.08e Spearman rank correlation5.08f Hypothesis test: Spearman rank |
| Footballer | Body Mass Index, \(\boldsymbol { x }\) | Time taken to complete the obstacle course, \(y\) seconds |
| A | 18.7 | 690 |
| B | 19.5 | 801 |
| C | 20.2 | 723 |
| D | 20.4 | 633 |
| E | 20.8 | 660 |
| F | 21.9 | 655 |
| G | 23.2 | 711 |
| H | 24.3 | 642 |
| I | 24.8 | 607 |
\begin{enumerate}
\item A random sample of 9 footballers is chosen to participate in an obstacle course. The time taken, $y$ seconds, for each footballer to complete the obstacle course is recorded, together with the footballer's Body Mass Index, $x$. The results are shown in the table below.
\end{enumerate}
\begin{center}
\begin{tabular}{|l|l|l|}
\hline
Footballer & Body Mass Index, $\boldsymbol { x }$ & Time taken to complete the obstacle course, $y$ seconds \\
\hline
A & 18.7 & 690 \\
\hline
B & 19.5 & 801 \\
\hline
C & 20.2 & 723 \\
\hline
D & 20.4 & 633 \\
\hline
E & 20.8 & 660 \\
\hline
F & 21.9 & 655 \\
\hline
G & 23.2 & 711 \\
\hline
H & 24.3 & 642 \\
\hline
I & 24.8 & 607 \\
\hline
\end{tabular}
\end{center}
Russell claims, that for footballers, as Body Mass Index increases the time taken to complete the obstacle course tends to decrease.\\
(a) Find, to 3 decimal places, Spearman's rank correlation coefficient between $x$ and $y$.\\
(b) Use your value of Spearman's rank correlation coefficient to test Russell's claim. Use a 5\% significance level and state your hypotheses clearly.
The product moment correlation coefficient for these data is - 0.5594\\
(c) Use the value of the product moment correlation coefficient to test for evidence of a negative correlation between Body Mass Index and the time taken to complete the obstacle course. Use a 5\% significance level.\\
(d) Using your conclusions to part (b) and part (c), describe the relationship between Body Mass Index and the time taken to complete the obstacle course.
\hfill \mbox{\textit{Edexcel S3 2018 Q1 [12]}}