| Exam Board | CAIE |
|---|---|
| Module | Further Paper 4 (Further Paper 4) |
| Year | 2021 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Wilcoxon tests |
| Type | Wilcoxon matched-pairs signed-rank test |
| Difficulty | Standard +0.3 This is a straightforward application of the Wilcoxon matched-pairs signed-rank test with clear paired data. Students must calculate differences, rank absolute values, sum ranks for positive/negative differences, and compare to critical values. While it requires careful arithmetic and knowledge of the test procedure, it's a standard textbook exercise with no conceptual challenges or novel problem-solving—slightly easier than average for Further Maths statistics. |
| Spec | 5.07b Sign test: and Wilcoxon signed-rank |
| Chocolate | A | B | C | D | E | F | G | H | I |
| Taster 1 | 72 | 86 | 75 | 92 | 98 | 79 | 87 | 60 | 62 |
| Taster 2 | 84 | 72 | 74 | 95 | 85 | 87 | 82 | 75 | 68 |
| Answer | Marks | Guidance |
|---|---|---|
| 2 | H : difference in population medians = 0 (m = m ) | |
| 0 a b | B1 | Correct hypotheses, allow m . Do not allow μ or mean. |
| Answer | Marks | Guidance |
|---|---|---|
| 1 a b | B1 | ‘population’ included. |
| Diff: 12 −14 −1 3 −13 8 −5 15 6 | M1 | Allow one error. |
| Rank: 6 −8 −1 2 −7 5 −3 9 4 | M1 | Allow one error. |
| Smaller sum 19 | A1 | (Other sum is 26.) |
| Answer | Marks | Guidance |
|---|---|---|
| 0 | M1 | Comparison with 8 and correct FT conclusion. |
| There is insufficient evidence that marks differ | A1 | Correct conclusion, in context, following correct work, except |
| Answer | Marks | Guidance |
|---|---|---|
| Question | Answer | Marks |
Question 2:
2 | H : difference in population medians = 0 (m = m )
0 a b | B1 | Correct hypotheses, allow m . Do not allow μ or mean.
d
H : difference in population medians ≠ 0 (m ≠ m )
1 a b | B1 | ‘population’ included.
Diff: 12 −14 −1 3 −13 8 −5 15 6 | M1 | Allow one error.
Rank: 6 −8 −1 2 −7 5 −3 9 4 | M1 | Allow one error.
Smaller sum 19 | A1 | (Other sum is 26.)
Critical tabular value = 8
‘19’ > 8 so accept H
0 | M1 | Comparison with 8 and correct FT conclusion.
There is insufficient evidence that marks differ | A1 | Correct conclusion, in context, following correct work, except
possibly the hypotheses. Level of uncertainty in language is
used.
7
Question | Answer | Marks | GuidanceA company is developing a new flavour of chocolate by varying the quantities of the ingredients. A random selection of 9 flavours of chocolate are judged by two tasters who each give marks out of 100 to each flavour of chocolate.
\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|}
\hline
Chocolate & A & B & C & D & E & F & G & H & I \\
\hline
Taster 1 & 72 & 86 & 75 & 92 & 98 & 79 & 87 & 60 & 62 \\
\hline
Taster 2 & 84 & 72 & 74 & 95 & 85 & 87 & 82 & 75 & 68 \\
\hline
\end{tabular}
Carry out a Wilcoxon matched-pairs signed-rank test at the 10% significance level to investigate whether, on average, there is a difference between marks awarded by the two tasters. [7]
\hfill \mbox{\textit{CAIE Further Paper 4 2021 Q2 [7]}}