| Exam Board | OCR |
|---|---|
| Module | Further Statistics (Further Statistics) |
| Session | Specimen |
| 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 and small sample size (n=7). Students must calculate differences, rank absolute values, apply the test statistic, and compare to critical values from tables. Part (ii) requires basic understanding of test properties. While it involves multiple steps, it's a standard textbook procedure with no novel insight required, making it slightly easier than average for Further Maths statistics. |
| Spec | 5.07b Sign test: and Wilcoxon signed-rank |
| Elder twin | 65 | 37 | 60 | 79 | 39 | 40 | 88 |
| Younger twin | 58 | 39 | 61 | 62 | 50 | 26 | 84 |
| Answer | Marks | Guidance |
|---|---|---|
| 4 | (i) | 7 2 1 17 11 14 4 |
| Answer | Marks |
|---|---|
| difference in test scores | M1 |
| Answer | Marks |
|---|---|
| [6] | 1.1 |
| Answer | Marks |
|---|---|
| i | Calculate differences, rank them and |
| Answer | Marks |
|---|---|
| crit | Follow through with correct |
| Answer | Marks | Guidance |
|---|---|---|
| 4 | (ii) | Uses magnitude of differences oe |
| Answer | Marks | Guidance |
|---|---|---|
| [1] | 3.5b | |
| 4 | 2 | 1 |
| + | – | – |
| 4 | 5.4431 | 0.3826 |
| Answer | Marks | Guidance |
|---|---|---|
| 4(i) | 2 | 20 |
| Answer | Marks | Guidance |
|---|---|---|
| 4(ii) | 0 | 0 |
Question 4:
4 | (i) | 7 2 1 17 11 14 4
4 2 1 7 6 5 3
+ – – + – + +
H :population median difference (cid:32)0
0
H :population median difference (cid:122)0
1
P(cid:32)4(cid:14)7(cid:14)5(cid:14)3(cid:32)19
Q(cid:32)1(cid:14)2(cid:14)6(cid:32)9
T (cid:32)8
T (cid:32)3; 8(cid:33)3
crit
Do not reject H . Insufficient evidence of a
0
difference in test scores | M1
B1
A1
A1
B1
A1FT
[6] | 1.1
2.5
3.3
3.4
1.1
2.2b
i | Calculate differences, rank them and
attach signs
Hypothesescorrectly stated
n
e
P or Q correct
Both P and Q seen, T correct
m
Comparison with correct T
crit
Correct conclusion, in context,
acknowledge uncertainty
FT their T but not their T
crit | Follow through with correct
signs and ranks from incorrect
differences
SC3: Two-sample, max 3/6
4 | (ii) | Uses magnitude of differences oe | c
B1
[1] | 3.5b
4 | 2 | 1 | 7 | 6 | 5 | 3
+ | – | – | + | – | + | +
4 | 5.4431 | 0.3826
--- 4(i) ---
4(i) | 2 | 20 | 2 | 6
--- 4(ii) ---
4(ii) | 0 | 0 | 01 | 14 A psychologist investigated the scores of pairs of twins on an aptitude test. Seven pairs of twins were chosen randomly, and the scores are given in the following table.
\begin{center}
\begin{tabular}{ | l | l | l | l | l | l | l | l | }
\hline
Elder twin & 65 & 37 & 60 & 79 & 39 & 40 & 88 \\
\hline
Younger twin & 58 & 39 & 61 & 62 & 50 & 26 & 84 \\
\hline
\end{tabular}
\end{center}
(i) Carry out an appropriate Wilcoxon test at the $10 \%$ significance level to investigate whether there is evidence of a difference in test scores between the elder and the younger of a pair of twins.\\
(ii) Explain the advantage in this case of a Wilcoxon test over a sign test.
\hfill \mbox{\textit{OCR Further Statistics Q4 [7]}}