| Exam Board | OCR |
|---|---|
| Module | S4 (Statistics 4) |
| Year | 2008 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Wilcoxon tests |
| Type | Sign test |
| Difficulty | Standard +0.3 This is a straightforward application of the sign test with clear data presentation. Students need to recognize that the Wilcoxon test requires symmetry (part i), then execute a standard sign test procedure counting values above/below the median and using binomial tables. The stem-and-leaf diagram makes counting easy, and the test is routine S4 material requiring no novel insight. |
| Spec | 5.07b Sign test: and Wilcoxon signed-rank |
| 14 | 1 | 2 | |||||||
| 15 | 2 | 4 | |||||||
| 16 | 0 | 3 | 6 | ||||||
| 17 | 1 | 5 | 7 | ||||||
| 18 | 3 | 4 | 5 | 7 | 9 | ||||
| 19 | 2 | 4 | 6 | 7 | 8 | 9 | |||
| 20 | 0 | 1 | 3 | 4 | 5 | 7 | 8 | 9 | |
| 21 | 7 |
| Answer | Marks | Guidance |
|---|---|---|
| (i) Show graph indicating attempt at reflection in \(y = x\) | M1 | with correct curvature and crossing negative y-axis and positive x-axis |
| Show correct graph with x-coord 2 and y-coord -3 indicated | A1 | |
| (ii) Show graph indicating attempt at reflection in x-axis | M1 | with correct curvature and crossing each negative axis |
| Show correct graph with x-coord -3 indicated | A1 | |
| ... and y-coord -4 indicated | A1 | |
| [SC: Incorrect curve earning M0 but both correct intercepts indicated] | B1] |
(i) Show graph indicating attempt at reflection in $y = x$ | M1 | with correct curvature and crossing negative y-axis and positive x-axis
Show correct graph with x-coord 2 and y-coord -3 indicated | A1 |
(ii) Show graph indicating attempt at reflection in x-axis | M1 | with correct curvature and crossing each negative axis
Show correct graph with x-coord -3 indicated | A1 |
... and y-coord -4 indicated | A1 |
[SC: Incorrect curve earning M0 but both correct intercepts indicated] | B1] |2 Part of Helen's psychology dissertation involved the reaction times to a certain stimulus. She measured the reaction times of 30 randomly selected students, in seconds correct to 2 decimal places. The results are shown in the following stem-and-leaf diagram.
\begin{center}
\begin{tabular}{ l | l l l l l l l l l }
14 & 1 & 2 & & & & & & & \\
15 & 2 & 4 & & & & & & & \\
16 & 0 & 3 & 6 & & & & & & \\
17 & 1 & 5 & 7 & & & & & & \\
18 & 3 & 4 & 5 & 7 & 9 & & & & \\
19 & 2 & 4 & 6 & 7 & 8 & 9 & & & \\
20 & 0 & 1 & 3 & 4 & 5 & 7 & 8 & 9 & \\
21 & 7 & & & & & & & & \\
\end{tabular}
\end{center}
Key: 18 | 3 means 1.83 seconds
Helen wishes to test whether the population median time exceeds 1.80 seconds.\\
(i) Give a reason why the Wilcoxon signed-rank test should not be used.\\
(ii) Carry out a suitable non-parametric test at the $5 \%$ significance level.
\hfill \mbox{\textit{OCR S4 2008 Q2 [8]}}