| Exam Board | OCR MEI |
|---|---|
| Module | Further Statistics Minor (Further Statistics Minor) |
| Session | Specimen |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Hypothesis test of Spearman’s rank correlation coefficien |
| Type | Effect of data changes |
| Difficulty | Standard +0.3 This is a standard Spearman's rank correlation question with routine calculations and a straightforward hypothesis test. Part (i) requires basic interpretation, parts (ii-iii) are textbook procedures (ranking, formula application, comparing to critical values), and part (iv) tests understanding of when Pearson vs Spearman is appropriate. The 10-mark allocation and multi-part structure are typical, but no novel insight or complex reasoning is required—slightly easier than average due to its procedural nature. |
| Spec | 5.08e Spearman rank correlation5.08f Hypothesis test: Spearman rank |
| Contestant | A | B | C | D | E | F | G |
| Age | 66 | 51 | 39 | 29 | 9 | 22 | 14 |
| Score | 12 | 11 | 15 | 17 | 16 | 18 | 9 |
| Answer | Marks | Guidance |
|---|---|---|
| 5 | (i) | Spearman’s correlation coefficient will become more |
| Answer | Marks | Guidance |
|---|---|---|
| down as age goes up. | E1 | |
| [1] | 2.4 | oe |
| Answer | Marks | Guidance |
|---|---|---|
| 5 | (ii) | Contestant A B C D E F |
| Answer | Marks |
|---|---|
| S | M1 |
| Answer | Marks |
|---|---|
| [3] | 1.1 |
| Answer | Marks |
|---|---|
| 1.1 | N |
| Answer | Marks |
|---|---|
| BC | can be reversed as long as |
| Answer | Marks | Guidance |
|---|---|---|
| 5 | (iii) | H : there is no association between age and score. |
| Answer | Marks |
|---|---|
| that there is association between age and score. | B1 |
| Answer | Marks |
|---|---|
| [5] | M |
| Answer | Marks |
|---|---|
| 2.2b | B1 for H |
| Answer | Marks |
|---|---|
| r | < 1 |
| Answer | Marks |
|---|---|
| value | hypotheses as shown in |
| Answer | Marks | Guidance |
|---|---|---|
| 5 | (iv) | S |
| Cannot tell if it is bivariate Normal | E1 | |
| [1] | 3.5b | E.g. score must be an integer |
| Contestant | A | B |
| Age rank | 6 | 5 |
| Score rank | 2 | 1 |
Question 5:
5 | (i) | Spearman’s correlation coefficient will become more
negative as there is a stronger tendency for score to go
down as age goes up. | E1
[1] | 2.4 | oe | Saying it is closer to a
straight line does not get
the mark.
5 | (ii) | Contestant A B C D E F
Age rank 6 5 4 3 1 2
Score rank 2 1 3 5 4 6
r = –0.7714 (4 s.f.)
S | M1
M1
A1
[3] | 1.1
1.1
1.1 | N
For ranking Age
EFor ranking Score
BC | can be reversed as long as
consistent
can be reversed as long as
consistent
5 | (iii) | H : there is no association between age and score.
0
H : there is an association between age and score.
1
For n = 6 5% critical value is 0.8857
E
Since 0.7714< 0.8857
P
Do not reject the null hypothesis
There is insufficient evidence to suggest at the 5% level
that there is association between age and score. | B1
B1
I
C
B1
M1
A1FT
[5] | M
3.3
2.5
3.4
1.1
2.2b | B1 for H
0
B1 for H and population soi
1
NB H H not in terms of ρ
0 1
B1 for (cid:114) 0.8857
M1 for comparison with
critical value, provided
|r| < 1
s
A1 for conclusion in words FT
their r and sensible critical
s
value | hypotheses as shown in
the answer column should
be understood to imply
population
5 | (iv) | S
Cannot tell if it is bivariate Normal | E1
[1] | 3.5b | E.g. score must be an integer
Contestant | A | B | C | D | E | F
Age rank | 6 | 5 | 4 | 3 | 1 | 2
Score rank | 2 | 1 | 3 | 5 | 4 | 6Each contestant in a talent competition is given a score out of $20$ by a judge. The organisers suspect that the judge's scores are associated with the age of the contestant. Table $5.1$ and the scatter diagram in Fig. $5.2$ show the scores and ages of a random sample of $7$ contestants.
\begin{tabular}{|c|c|c|c|c|c|c|c|}
\hline
Contestant & A & B & C & D & E & F & G \\
\hline
Age & 66 & 51 & 39 & 29 & 9 & 22 & 14 \\
\hline
Score & 12 & 11 & 15 & 17 & 16 & 18 & 9 \\
\hline
\end{tabular}
\textbf{Table 5.1}
\includegraphics{figure_1}
\textbf{Fig. 5.2}
Contestant G did not finish her performance, so it is decided to remove her data.
\begin{enumerate}[label=(\roman*)]
\item Spearman's rank correlation coefficient between age and score, including all $7$ contestants, is $-0.25$. Explain why Spearman's rank correlation coefficient becomes more negative when the data for contestant G is removed. [1]
\item Calculate Spearman's rank correlation coefficient for the $6$ remaining contestants. [3]
\item Using this value of Spearman's rank correlation coefficient, carry out a hypothesis test at the $5\%$ level to investigate whether there is any association between age and score. [5]
\item Briefly explain why it may be inappropriate to carry out a hypothesis test based on Pearson's product moment correlation coefficient using these data. [1]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Further Statistics Minor Q5 [10]}}