| Exam Board | OCR MEI |
|---|---|
| Module | Further Statistics A AS (Further Statistics A AS) |
| Year | 2022 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Hypothesis test of Spearman’s rank correlation coefficien |
| Type | Hypothesis test for association |
| Difficulty | Standard +0.3 This is a straightforward application of Spearman's rank correlation test with clear data provided. Students must identify non-linearity from a scatter diagram (routine interpretation), calculate ranks and apply the standard formula, then perform a hypothesis test using critical value tables. All steps are standard textbook procedures with no novel problem-solving required, though it does require careful calculation with 10 data points. |
| Spec | 5.08e Spearman rank correlation5.08f Hypothesis test: Spearman rank |
| Answer | Marks | Guidance |
|---|---|---|
| 3 | (a) | Because the scatter diagram does not appear to be |
| Answer | Marks |
|---|---|
| probably not bivariate Normal. | E1* |
| Answer | Marks |
|---|---|
| [2] | 3.5b |
| 3.5b | For not elliptical |
| Answer | Marks | Guidance |
|---|---|---|
| 3 | (b) | Rank PC 1 3 2 4 6 5 8 10 7 9 |
| Answer | Marks | Guidance |
|---|---|---|
| 165 | Rank PC | 1 |
| Answer | Marks |
|---|---|
| [3] | 1.1 |
| Answer | Marks |
|---|---|
| 1.1 | For ranking DW |
| Answer | Marks | Guidance |
|---|---|---|
| Rank DW | 1 | 2 |
| 3 | (c) | H : There is no association between percentage |
| Answer | Marks |
|---|---|
| dry weight in the population. | B1 |
| Answer | Marks |
|---|---|
| [5] | 2.5 |
| Answer | Marks |
|---|---|
| 2.2b | For hypotheses in context |
| Answer | Marks | Guidance |
|---|---|---|
| provided | r | < 1 |
Question 3:
3 | (a) | Because the scatter diagram does not appear to be
elliptical (but instead a curve) so the distribution is
probably not bivariate Normal. | E1*
E1dep*
[2] | 3.5b
3.5b | For not elliptical
For full answer (dependent on first mark)
If no E marks awarded SC B1 for the association might not
be linear.
3 | (b) | Rank PC 1 3 2 4 6 5 8 10 7 9
Rank DW 1 2 3 4 5 6 7 8 9 10
( =151)
Spearman’s rank coefficient = 0.9152
165 | Rank PC | 1 | 3 | 2 | 4 | 6 | 5 | 8 | 10 | 7 | 9 | M1
M1
A1
[3] | 1.1
1.1
1.1 | For ranking DW
For ranking PC. Allow both ranks reversed
BC Allow 0.915, 0.92
Rank DW | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10
3 | (c) | H : There is no association between percentage
0
colonisation and shoot dry weight in the population
H : There is some association between percentage
1
colonisation and shoot dry weight in the population
(For n = 10, 2-tailed 5% critical value is) 0.6485
0.9152 > 0.6485
(Reject H ) There is evidence to suggest that there is
0
association between percentage colonisation and shoot
dry weight in the population. | B1
B1
B1
M1
A1
[5] | 2.5
1.2
3.4
1.1
2.2b | For hypotheses in context
For population seen in either of the hypotheses
Allow 0.649
For correct comparison of their r with their critical value
s
provided |r| < 1
s
For correct non-assertive conclusion in context.
FT their r but A0 if wrong critical value used.
s3 A biology student is doing an experiment in which plants are inoculated with a particular microorganism in an attempt to help them grow. She is investigating whether there is any association between the percentage of roots which have been colonised by the microorganism and the dry weight of the plant shoots. After the plants have grown for a few weeks, the student takes a random sample of 10 plants and measures the percentage of roots which have been colonised by the microorganism and the dry weight of the plant shoots.
The spreadsheet output shows the data, together with a scatter diagram to illustrate the data.\\
\includegraphics[max width=\textwidth, alt={}, center]{8f1e0c68-a334-4657-823e-386ab0994c02-3_722_1648_635_244}
\begin{enumerate}[label=(\alph*)]
\item The student decides that a test based on Pearson's product moment correlation coefficient may not be valid.
Explain why she comes to this conclusion.
\item Calculate the value of Spearman's rank correlation coefficient.
\item Carry out a test based on this coefficient, at the $5 \%$ significance level, to investigate whether there is any association between percentage colonisation and shoot dry weight.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Further Statistics A AS 2022 Q3 [10]}}