| Exam Board | WJEC |
|---|---|
| Module | Further Unit 2 (Further Unit 2) |
| Session | Specimen |
| Marks | 9 |
| 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 Spearman's rank correlation question requiring ranking data, calculating the coefficient using the formula, and performing a hypothesis test. While it involves multiple steps and is from Further Maths, the procedure is entirely routine with no conceptual challenges or novel problem-solving required—just careful arithmetic and table lookup. |
| Spec | 5.08e Spearman rank correlation5.08f Hypothesis test: Spearman rank5.08g Compare: Pearson vs Spearman |
| Student | A | B | C | D | E | F | G | H |
| History mark | 73 | 59 | 83 | 49 | 57 | 82 | 67 | 60 |
| Geography mark | 55 | 51 | 58 | 59 | 44 | 66 | 49 | 67 |
| Answer | Marks | Guidance |
|---|---|---|
| S | A | B |
| H | 3 | 6 |
| G | 5 | 6 |
| \(\sum d^2 = 64\) | M1, A1, A1, B1 | AO3, AO1, AO1, AO1 |
| \(r_s = 1 - \frac{6 \times 64}{8 \times 63} = 0.238(095238...)\) | M1, A1 | AO1, AO1 |
| (b) 5% 1-tail crit value = 0.6429. This suggests that there is no positive association between marks in History and marks in Geography. | B1, B1 | AO1, AO3 |
| (c) Because the data might not follow a bivariate normal distribution. | B1 | AO2 |
**(a)** The ranks are:
| S | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| H | 3 | 6 | 1 | 8 | 7 | 2 | 4 | 5 |
| G | 5 | 6 | 4 | 3 | 8 | 2 | 7 | 1 |
$\sum d^2 = 64$ | M1, A1, A1, B1 | AO3, AO1, AO1, AO1 | Attempt to find ranks; Correct values for 1st row; Correct values for 2nd row
$r_s = 1 - \frac{6 \times 64}{8 \times 63} = 0.238(095238...)$ | M1, A1 | AO1, AO1
**(b)** 5% 1-tail crit value = 0.6429. This suggests that there is no positive association between marks in History and marks in Geography. | B1, B1 | AO1, AO3
**(c)** Because the data might not follow a bivariate normal distribution. | B1 | AO2 | [9]
---A class of 8 students sit examinations in History and Geography. The marks obtained by these students are given below.
\begin{tabular}{|l|c|c|c|c|c|c|c|c|}
\hline
Student & A & B & C & D & E & F & G & H \\
\hline
History mark & 73 & 59 & 83 & 49 & 57 & 82 & 67 & 60 \\
\hline
Geography mark & 55 & 51 & 58 & 59 & 44 & 66 & 49 & 67 \\
\hline
\end{tabular}
\begin{enumerate}[label=(\alph*)]
\item Calculate Spearman's rank correlation coefficient for this data set. [6]
\item Hence determine whether or not, at the 5% significance level, there is evidence of a positive association between marks in History and marks in Geography. [2]
\item Explain why it might not have been appropriate to use Pearson's product moment correlation coefficient to test association using this data set. [1]
\end{enumerate}
\hfill \mbox{\textit{WJEC Further Unit 2 Q3 [9]}}