| Exam Board | OCR MEI |
|---|---|
| Module | Further Statistics B AS (Further Statistics B AS) |
| Year | 2021 |
| Session | November |
| Marks | 9 |
| 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 hypotheses (testing if median > 12.7). Students must calculate differences, rank them, find the test statistic, and compare to critical values. While it requires careful arithmetic and knowledge of the procedure, it's a standard textbook exercise with no novel insight required. The assumption question in part (b) is routine recall. |
| Spec | 5.07b Sign test: and Wilcoxon signed-rank |
| Answer | Marks | Guidance |
|---|---|---|
| 4 | (a) | Wilcoxon signed-rank test |
| Answer | Marks |
|---|---|
| Time | Time |
| Answer | Marks |
|---|---|
| 12.7 12.7 |
| Answer | Marks |
|---|---|
| time has increased. | B1 |
| Answer | Marks |
|---|---|
| [8] | 1.1a |
| Answer | Marks |
|---|---|
| 3.5a | Can be implied by correct procedure |
| Answer | Marks | Guidance |
|---|---|---|
| 4 | (b) | The underlying distribution is symmetrical |
| [1] | 1.2 | |
| Time | Time |
| Answer | Marks | Guidance |
|---|---|---|
| 12.7 | Time |
| Answer | Marks | Guidance |
|---|---|---|
| 12.7 | Rank | |
| 12.63 | -0.07 | 0.07 |
| 13.24 | 0.54 | 0.54 |
| 11.73 | -0.97 | 0.97 |
| 14.91 | 2.21 | 2.21 |
| 13.17 | 0.47 | 0.47 |
| 13.53 | 0.83 | 0.83 |
| 12.33 | -0.37 | 0.37 |
| 14.27 | 1.57 | 1.57 |
| 11.48 | -1.22 | 1.22 |
| 13.51 | 0.81 | 0.81 |
| 13.05 | 0.35 | 0.35 |
| 13.83 | 1.13 | 1.13 |
Question 4:
4 | (a) | Wilcoxon signed-rank test
H : population median is 12.7
0
H : population median is greater than 12.7
1
Time |Time
Time − − Rank
12.7 12.7|
12.63 -0.07 0.07 1
13.24 0.54 0.54 5
11.73 -0.97 0.97 8
14.91 2.21 2.21 12
13.17 0.47 0.47 4
13.53 0.83 0.83 7
12.33 -0.37 0.37 3
14.27 1.57 1.57 11
11.48 -1.22 1.22 10
13.51 0.81 0.81 6
13.05 0.35 0.35 2
13.83 1.13 1.13 9
W = 1 + 8 + 3 + 10 = 22
-
(W = 5 + 12 + 4 + 7 + 11 + 6 + 2 + 9 = 56)
+
Test statistic = W = 22
-
Critical value = 17
So do not reject H
0
Insufficient evidence to suggest that download
time has increased. | B1
B1
B1
M1
M1
A1
B1
A1
[8] | 1.1a
3.3
2.1
1.1
1.1
1.1
3.4
3.5a | Can be implied by correct procedure
being carried out
Population median used
Both correct
For attempt at ranking
Attempt to calculate either W or W
+ -
Do not FT incorrect test statistic or
critical value
4 | (b) | The underlying distribution is symmetrical | E1
[1] | 1.2
Time | Time
−
12.7 | |Time
−
12.7| | Rank
12.63 | -0.07 | 0.07 | 1
13.24 | 0.54 | 0.54 | 5
11.73 | -0.97 | 0.97 | 8
14.91 | 2.21 | 2.21 | 12
13.17 | 0.47 | 0.47 | 4
13.53 | 0.83 | 0.83 | 7
12.33 | -0.37 | 0.37 | 3
14.27 | 1.57 | 1.57 | 11
11.48 | -1.22 | 1.22 | 10
13.51 | 0.81 | 0.81 | 6
13.05 | 0.35 | 0.35 | 2
13.83 | 1.13 | 1.13 | 94 John regularly downloads podcasts onto his mobile phone. From past experience he knows that the average time to download one 30 -minute podcast is 12.7 s . He believes that this time has recently increased. At each of 12 randomly chosen times, he downloads a 30-minute podcast. The times in seconds to download the 12 podcasts are as follows.\\
$\begin{array} { l l l l l l l l l l l } 12.63 & 13.24 & 11.73 & 14.91 & 13.17 & 13.53 & 12.33 & 14.27 & 11.48 & 13.51 & 13.05 \end{array} 13.83$
\begin{enumerate}[label=(\alph*)]
\item Given that it is not known whether the times are Normally distributed, carry out a suitable test at the $5 \%$ significance level to investigate whether the average download time has increased.
\item What assumption is required to carry out the test in part (a)?
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Further Statistics B AS 2021 Q4 [9]}}