| Exam Board | OCR |
|---|---|
| Module | S4 (Statistics 4) |
| Year | 2014 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Wilcoxon tests |
| Type | Critical region or test statistic properties |
| Difficulty | Standard +0.3 This question tests basic understanding of the Wilcoxon rank-sum test properties. Part (i) requires knowing that W is the sum of ranks for one sample, with minimum value being 1+2+...+11=66. Part (ii) involves looking up critical values in tables. Both parts are straightforward recall and table-reading with minimal calculation, making this easier than average for A-level statistics. |
| Spec | 5.07b Sign test: and Wilcoxon signed-rank |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(1 + 2 + \ldots + 11 = 66\) | M1 | M0 if followed by incorrect work |
| \(= 66\) | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \((N)(132, 264)\) | B1 | |
| \(\dfrac{(W + 0.5 - \text{"132"})}{\sqrt{\text{"264"}}}\) | M1 | Allow wrong, or no, continuity correction. Allow reversed if consistent. OR \(132(-0.5) \pm z\times\sqrt{264}\) M1; \(z=2.576\) or \(2.58\) B1; \((89.6,[173.4])\) A1 |
| \(< -\) | M1* | May be earned later |
| \(2.576\) | B1 | Allow 2.58. \(\leq 89\) A1. Allow if lower limit only considered |
| Solve inequality | *M1 | or equation if final answer uses \(<\) or \(\leq\). Integer needed |
| \(< 89.6\;\;(66 \leq)\; W \leq 89\) | A1 |
# Question 6:
## Part (i)
| Answer | Marks | Guidance |
|--------|-------|----------|
| $1 + 2 + \ldots + 11 = 66$ | M1 | M0 if followed by incorrect work |
| $= 66$ | A1 | |
## Part (ii)
| Answer | Marks | Guidance |
|--------|-------|----------|
| $(N)(132, 264)$ | B1 | |
| $\dfrac{(W + 0.5 - \text{"132"})}{\sqrt{\text{"264"}}}$ | M1 | Allow wrong, or no, continuity correction. Allow reversed if consistent. OR $132(-0.5) \pm z\times\sqrt{264}$ M1; $z=2.576$ or $2.58$ B1; $(89.6,[173.4])$ A1 |
| $< -$ | M1* | May be earned later |
| $2.576$ | B1 | Allow 2.58. $\leq 89$ A1. Allow if lower limit only considered |
| Solve inequality | *M1 | or equation if final answer uses $<$ or $\leq$. Integer needed |
| $< 89.6\;\;(66 \leq)\; W \leq 89$ | A1 | |
---6 A Wilcoxon rank-sum test with samples of sizes 11 and 12 is carried out.\\
(i) What is the least possible value of the test statistic $W$ ?\\
(ii) The null hypothesis is that the two samples came from identical populations. Given that the null hypothesis was rejected at the $1 \%$ level using a 2 -tail test, find the set of possible values of $W$.
\hfill \mbox{\textit{OCR S4 2014 Q6 [8]}}