| Exam Board | Edexcel |
|---|---|
| Module | FS2 AS (Further Statistics 2 AS) |
| Year | 2024 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Wilcoxon tests |
| Type | Spearman's rank correlation test |
| Difficulty | Standard +0.3 This is a straightforward application of Spearman's rank correlation test with clear hypotheses, a small dataset (n=8), and standard critical value lookup at 1% significance. The ranking and calculation are routine for Further Statistics students, though slightly above average difficulty due to being a hypothesis test rather than pure calculation. |
| Spec | 5.08f Hypothesis test: Spearman rank |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(H_0: \rho_s = 0 \quad H_1: \rho_s < 0\) | B1 | Both hypotheses correct in terms of \(\rho_s\) or \(\rho\) |
| Ranks computed; \(d^2\) values: \(36, 36, 4, 4, 4, 4, 25, 49\); \(\sum d^2 = 162\) | M1, dM1 | 1st M1: attempt to rank both rows (at least 4 correct in one row or 2 pairs). 2nd dM1: dependent on 1st M1, attempt at \(d\) or \(d^2\) row |
| \(r_s = 1 - \frac{6 \times \text{"their } \sum d^2\text{"} }{8(8^2-1)}\) | M1 | Allow independently of 1st M1 and 2nd dM1 |
| \(r_s = -0.9285\ldots\) awrt \(\mathbf{-0.929}\) | A1 | awrt \(-0.929\); allow \(-\frac{13}{14}\) or \(-0.928\) following correct expression. Allow \(+0.929\) following correct reverse ranking with \(\sum d^2 = 6\) |
| Critical value \(-0.8333\) | B1 | Correct critical value (allow \(\pm 0.8333\)); 4dp acceptable but allow 3 in 2nd A1 |
| Reject \(H_0\); there is sufficient evidence to suggest the data shows negative rank correlation | A1ft | Dependent on all M marks and \( |
# Question 2:
| Answer/Working | Marks | Guidance |
|---|---|---|
| $H_0: \rho_s = 0 \quad H_1: \rho_s < 0$ | B1 | Both hypotheses correct in terms of $\rho_s$ or $\rho$ |
| Ranks computed; $d^2$ values: $36, 36, 4, 4, 4, 4, 25, 49$; $\sum d^2 = 162$ | M1, dM1 | 1st M1: attempt to rank both rows (at least 4 correct in one row or 2 pairs). 2nd dM1: dependent on 1st M1, attempt at $d$ or $d^2$ row |
| $r_s = 1 - \frac{6 \times \text{"their } \sum d^2\text{"} }{8(8^2-1)}$ | M1 | Allow independently of 1st M1 and 2nd dM1 |
| $r_s = -0.9285\ldots$ awrt $\mathbf{-0.929}$ | A1 | awrt $-0.929$; allow $-\frac{13}{14}$ or $-0.928$ following correct expression. Allow $+0.929$ following correct reverse ranking with $\sum d^2 = 6$ |
| Critical value $-0.8333$ | B1 | Correct critical value (allow $\pm 0.8333$); 4dp acceptable but allow 3 in 2nd A1 |
| Reject $H_0$; there is sufficient evidence to suggest the data shows negative rank correlation | A1ft | Dependent on all M marks and $|r_s| = 0.929$ or $|cv| = 0.833$ or better. No incorrect statements |\begin{enumerate}
\item A random sample of size $n = 8$ of paired data is taken from a population. The data are plotted below.\\
\includegraphics[max width=\textwidth, alt={}, center]{ba41c616-0805-4466-81b8-b985b0bdd94b-06_572_983_335_541}
\end{enumerate}
Test, at the $1 \%$ level of significance, whether or not there is evidence of a negative rank correlation between the two variables.
You should state your hypotheses and critical value and show your working clearly.
\hfill \mbox{\textit{Edexcel FS2 AS 2024 Q2 [7]}}