| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2002 |
| Session | June |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Hypothesis test of Spearman’s rank correlation coefficien |
| Type | Justify use of Spearman's |
| Difficulty | Standard +0.3 This is a standard textbook application of Spearman's rank correlation coefficient requiring ranking data, applying the formula Σd²/n(n²-1), and performing a hypothesis test using critical value tables. While it involves multiple steps (ranking, calculation, hypothesis test), each step follows a routine procedure with no novel insight required. The question is slightly easier than average because it's a direct application of a well-practiced technique with clear structure. |
| Spec | 5.08e Spearman rank correlation5.08f Hypothesis test: Spearman rank |
| Athlete | Performance | Dedication |
| A | 86 | 72 |
| B | 60 | 69 |
| C | 78 | 59 |
| D | 56 | 68 |
| E | 80 | 80 |
| F | 66 | 84 |
| G | 31 | 65 |
| H | 59 | 55 |
| I | 73 | 79 |
| J | 49 | 53 |
| Answer | Marks |
|---|---|
| \(\sum d^2 = 70\) | M1 |
| \(r_s = 1 - \frac{6 \times 70}{10 \times 99} = 0.576\) | M1 A1 (5) |
| Answer | Marks |
|---|---|
| \(H_0: \rho = 0; H_1: \rho \neq 0\) | B1 B1 |
| \(n = 10 \Rightarrow \text{critical value} = 0.5636\) | B1 |
| \(0.576 \text{ is in the critical region}\) | M1 |
| Evidence of correlation between performance and dedication. | A1ft (5) |
| Answer | Marks |
|---|---|
| Likely to be an element of judgement in grading. Dedication unlikely to be normally distributed. | B1 (1) |
| Total: 11 marks |
## Part (a)
| $\sum d^2 = 70$ | M1 | |
| $r_s = 1 - \frac{6 \times 70}{10 \times 99} = 0.576$ | M1 A1 (5) | |
## Part (b)
| $H_0: \rho = 0; H_1: \rho \neq 0$ | B1 B1 | |
| $n = 10 \Rightarrow \text{critical value} = 0.5636$ | B1 | |
| $0.576 \text{ is in the critical region}$ | M1 | |
| Evidence of correlation between performance and dedication. | A1ft (5) | |
## Part (c)
| Likely to be an element of judgement in grading. Dedication unlikely to be normally distributed. | B1 (1) | |
| **Total: 11 marks** | | |
---At the end of a season an athletics coach graded a random sample of ten athletes according to their performances throughout the season and their dedication to training. The results, expressed as percentages, are shown in the table below.
\begin{center}
\begin{tabular}{|c|c|c|}
\hline
Athlete & Performance & Dedication \\
\hline
A & 86 & 72 \\
B & 60 & 69 \\
C & 78 & 59 \\
D & 56 & 68 \\
E & 80 & 80 \\
F & 66 & 84 \\
G & 31 & 65 \\
H & 59 & 55 \\
I & 73 & 79 \\
J & 49 & 53 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Calculate the Spearman rank correlation coefficient between performance and dedication. [5]
\item Stating clearly your hypotheses and using a 10\% level of significance, interpret your rank correlation coefficient. [5]
\item Give a reason to support the use of the rank correlation coefficient rather than the product moment correlation coefficient with these data. [1]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S3 2002 Q4 [11]}}