| Exam Board | OCR MEI |
|---|---|
| Module | Further Statistics B AS (Further Statistics B AS) |
| Session | Specimen |
| Marks | 8 |
| 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 data and standard procedure. Students must state the symmetry assumption, calculate differences from 720g, rank absolute differences, sum ranks, and compare to critical values. While it requires careful execution of multiple steps, it's a routine textbook exercise with no conceptual challenges beyond following the standard algorithm. |
| Spec | 5.07b Sign test: and Wilcoxon signed-rank |
| 705 | 730 | 720 | 691 | 718 | 680 |
| 731 | 723 | 745 | 708 | 724 | 736 |
| Answer | Marks | Guidance |
|---|---|---|
| 4 | (i) | Underlying distribution is symmetrical |
| [1] | 1.2 | |
| 4 | (ii) | H : population median is 720g |
| Answer | Marks |
|---|---|
| mass of hedgehogs is 720g. | B1 |
| Answer | Marks |
|---|---|
| [7] | 3.3 |
| Answer | Marks |
|---|---|
| 3.5a | Population median used in |
| Answer | Marks |
|---|---|
| Mass | Mass |
Question 4:
4 | (i) | Underlying distribution is symmetrical | E1
[1] | 1.2
4 | (ii) | H : population median is 720g
0
H : population median is not 720g
1
Mass Mass
–720
705 –15 15 7
730 10 10 4
720 0 0
691 –29 29 10
718 –2 2 1
680 –40 40 11
731 11 11 5
723 3 3 2
745 25 25 9
708 –12 12 6
E
724 4 4 3
736 16 16 8
W (cid:32)4(cid:14)5(cid:14)2(cid:14)9(cid:14)3(cid:14)8(cid:32)31
(cid:14) P
W (cid:32)7(cid:14)10(cid:14)1(cid:14)11(cid:14)6(cid:32)35
(cid:16)
Test statistic = 31
Critical value = 10 S
No evidence to reject null hypothesis that the median
mass of hedgehogs is 720g. | B1
B1
M1
C
M1
A1
B1
A1
[7] | 3.3
2.5
1.1
I
1.1
1.1
3.4
3.5a | Population median used in
hypothNeses
Both hypotheses correct
E
Ranks
M
Attempt to calculate both W W
+ -
Test statistic
Critical value
Conclusion in context
Mass | Mass
–7204 An online encyclopedia claims that the average mass of an adult European hedgehog is 720 g . In an investigation to check this average figure, the masses in grams of twelve randomly chosen adult European hedgehogs are measured and shown below.
\begin{center}
\begin{tabular}{ l l l l l l }
705 & 730 & 720 & 691 & 718 & 680 \\
731 & 723 & 745 & 708 & 724 & 736 \\
\end{tabular}
\end{center}
(i) What assumption is required to carry out a Wilcoxon test in this situation?\\
(ii) Given that this assumption is met, carry out a 2 -tail Wilcoxon test at the $5 \%$ level to test whether the median mass is 720 g . You should state your hypotheses and complete the table of calculations in the Printed Answer Booklet.
\hfill \mbox{\textit{OCR MEI Further Statistics B AS Q4 [8]}}