| Exam Board | OCR MEI |
|---|---|
| Module | Further Statistics Major (Further Statistics Major) |
| Year | 2019 |
| Session | June |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Non-parametric tests |
| Type | Normality assessment for test choice |
| Difficulty | Standard +0.3 This is a straightforward application question requiring interpretation of normality diagnostics (p=0.024 suggests non-normality, so use sign test), identification of experimental design flaws (no control group, no randomization, etc.), and execution of a basic sign test against a known median. All steps are routine for Further Statistics students with no novel problem-solving required. |
| Spec | 5.07a Non-parametric tests: when to use5.07b Sign test: and Wilcoxon signed-rank5.07e Test medians |
| Answer | Marks | Guidance |
|---|---|---|
| 8 | (a) | A Wilcoxon test should be carried out since a t test |
| Answer | Marks |
|---|---|
| from a Normal distribution | B1 |
| Answer | Marks |
|---|---|
| [3] | For conclusion of Wilcoxon |
| Answer | Marks | Guidance |
|---|---|---|
| 8 | (b) | There is no indication that her sample is random |
| Answer | Marks |
|---|---|
| with and without tea drinking could be obtained | E1 |
| Answer | Marks |
|---|---|
| [3] | 1 mark for each correct statement |
| Answer | Marks | Guidance |
|---|---|---|
| 8 | (c) | H : population median is 33.5 |
| Answer | Marks |
|---|---|
| arithmetic ability | B1 |
| Answer | Marks |
|---|---|
| [7] | Population median used |
Question 8:
8 | (a) | A Wilcoxon test should be carried out since a t test
requires the population to be Normally distributed,
but the Normal probability plot is not roughly
straight and the p-value is low
which both suggest that the data does not come
from a Normal distribution | B1
E1
E1
[3] | For conclusion of Wilcoxon
For either
For both and correct conclusion
8 | (b) | There is no indication that her sample is random
The students from whom the sample is taken may
not be representative of students in general
EG
Test scores may not be independent due to having
the same teaching.
Students at this school may be more or less able
than at other schools
The sample size is too small
The test requires a symmetrical distribution which
may not be the case (or median not equal to the
mean)
Accept possible improvements such as a paired
sample test might be more suitable, if scores both
with and without tea drinking could be obtained | E1
E1
E1
[3] | 1 mark for each correct statement
Allow any valid features
Do NOT allow ‘not independent’ with
no context
Needs to be more than ‘these students
may not have previously averaged 35’
Do not allow ‘It could be that many
students who previously sat the test
had drunk tea beforehand’
8 | (c) | H : population median is 33.5
0
H : population median is greater than 33.5
1
Abs Ran
Result Res 33.5
value k
26 7.5 7.5 7
28 5.5 5.5 6
29 4.5 4.5 5
30 3.5 3.5 4
31 2.5 2.5 3
32 1.5 1.5 2
34 0.5 0.5 1
42 8.5 8.5 8
49 15.5 15.5 9
54 20.5 20.5 10
55 21.5 21.5 11
56 22.5 22.5 12
61 27.5 27.5 13
W = 7 + 6 + 5 + 4 + 3 + 2 = 27
(W = 1 + 8 + 9 + 10 + 11 + 12 + 13 = 64)
+
Test statistic = W = 27
Critical value = 21
So do not reject H ; there is insufficient evidence
0
to suggest that the tea drinking improves
arithmetic ability | B1
B1
M1
M1
A1
B1
A1
[7] | Population median used
Both correct
Can get B1 for H : median is 33.5 (no
0
mention of population) but Max B1B0
if no mention of population
Zero for use of ‘average’
For attempt at ranking
Allow if they omit second column of
table but otherwise all correct
Attempt to calculate either W or W
+
For correct test statistic 27
For correct critical value 21
For conclusion in context; no FT from
incorrect test statistic or critical value
FT for A1 (Not B1) from two tailed
hypothesis and ‘correct’ CV of 17.
Zero marks for Normal distribution test8 A student doing a school project wants to test a claim which she read in a newspaper that drinking a cup of tea will improve a person's arithmetic skills.\\
She chooses 13 students from her school and gets each of them to drink a cup of tea. She then gives each of them an arithmetic test. She knows that the average score for this test in students of the same age group as those she has chosen is 33.5.\\
The scores of the students she tests, arranged in ascending order, are as follows.\\
$\begin{array} { l l l l l l l l l l l l l } 26 & 28 & 29 & 30 & 31 & 32 & 34 & 42 & 49 & 54 & 55 & 56 & 61 \end{array}$
The student decides to use software to draw a Normal probability plot for these data, and to carry out a Normality test as shown in Fig. 8.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{3a89edc4-ac93-4691-ade8-4d4665b55202-09_536_1234_792_244}
\captionsetup{labelformat=empty}
\caption{Fig. 8}
\end{center}
\end{figure}
\begin{enumerate}[label=(\alph*)]
\item The student uses the output from the software to help in deciding on a suitable hypothesis test to use for investigating the claim about drinking tea.\\
Explain what the student should conclude.
\item The student's teacher agrees with the student's choice of hypothesis test, but says that even this test may not be valid as there may be some unsatisfactory features in the student's project. Give three features that the teacher might identify as unsatisfactory.
\item Assuming that the student's procedures can be justified, carry out an appropriate test at the $5 \%$ significance level to investigate the claim about drinking tea.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Further Statistics Major 2019 Q8 [13]}}