| Exam Board | CAIE |
|---|---|
| Module | Further Paper 4 (Further Paper 4) |
| Year | 2020 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Wilcoxon tests |
| Type | Wilcoxon signed-rank test (single sample) |
| Difficulty | Standard +0.3 This is a straightforward application of the Wilcoxon signed-rank test with clear steps: calculate differences from the median, rank absolute differences, sum ranks, and compare to critical value. The procedure is mechanical with no conceptual challenges, though it requires careful arithmetic. Slightly easier than average since it's a standard textbook procedure with small sample size (n=10) making calculations manageable. |
| Spec | 5.07b Sign test: and Wilcoxon signed-rank |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(H_0\): population median is 6.40, \(H_1\): population median \(\neq\) 6.40 | B1 | |
| Calculate differences and signed ranks: differences: 0.04, −0.24, −0.78, −0.58, 0.11, 0.22, −0.21, 0.02, −0.06, −0.12; ranks: 2, −8, −10, −9, 4, 7, −6, 1, −3, −5 | M1A1 | |
| Test statistic \(= 4 + 7 + 2 + 1 = 14\) | A1 | |
| Compare with correct critical value 8 | M1 | |
| Accept \(H_0\): insufficient evidence to reject claim | A1 FT | FT *their* test statistic |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Symmetrically distributed about the median | B1 |
## Question 2:
### Part 2(a):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $H_0$: population median is 6.40, $H_1$: population median $\neq$ 6.40 | B1 | |
| Calculate differences and signed ranks: differences: 0.04, −0.24, −0.78, −0.58, 0.11, 0.22, −0.21, 0.02, −0.06, −0.12; ranks: 2, −8, −10, −9, 4, 7, −6, 1, −3, −5 | M1A1 | |
| Test statistic $= 4 + 7 + 2 + 1 = 14$ | A1 | |
| Compare with correct critical value 8 | M1 | |
| Accept $H_0$: insufficient evidence to reject claim | A1 FT | FT *their* test statistic |
### Part 2(b):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Symmetrically distributed about the median | B1 | |
---2 The times, in milliseconds, taken by a computer to perform a certain task were recorded on 10 randomly chosen occasions. The times were as follows.
$$\begin{array} { l l l l l l l l l l }
6.44 & 6.16 & 5.62 & 5.82 & 6.51 & 6.62 & 6.19 & 6.42 & 6.34 & 6.28
\end{array}$$
It is claimed that the median time to complete the task is 6.4 milliseconds.
\begin{enumerate}[label=(\alph*)]
\item Carry out a Wilcoxon signed-rank test at the $5 \%$ significance level to test this claim.
\item State an underlying assumption that is made when using a Wilcoxon signed-rank test.
\end{enumerate}
\hfill \mbox{\textit{CAIE Further Paper 4 2020 Q2 [7]}}