| Exam Board | OCR MEI |
|---|---|
| Module | Further Statistics Major (Further Statistics Major) |
| Session | Specimen |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Hypothesis test of Spearman’s rank correlation coefficien |
| Type | Compare with PMCC |
| Difficulty | Standard +0.3 This question tests understanding of when to use Spearman's vs Pearson's correlation and one-tail vs two-tail tests. It requires interpreting a scatter plot to identify outliers/non-linearity (suggesting Spearman's) and recognizing directional hypothesis language ('tendency for higher wages...older men' suggests one-tail). These are standard A-level Further Statistics concepts requiring judgment rather than calculation, slightly easier than average due to being purely conceptual with clear visual cues. |
| Spec | 5.08e Spearman rank correlation5.08f Hypothesis test: Spearman rank5.08g Compare: Pearson vs Spearman |
| Answer | Marks | Guidance |
|---|---|---|
| 6 | (i) | Shape of scatter diagram not approx. |
| Answer | Marks |
|---|---|
| for test using pmcc to be valid | B1 |
| Answer | Marks |
|---|---|
| [2] | 3.5a |
| 2.4 | OR |
| Answer | Marks | Guidance |
|---|---|---|
| 6 | (ii) | One-tail because evidence of a positive |
| relationship is sought | B1 | |
| [1] | 2.4 | E |
Question 6:
6 | (i) | Shape of scatter diagram not approx.
elliptical
so no evidence of bivariate Normal required
for test using pmcc to be valid | B1
B1
[2] | 3.5a
2.4 | OR
B1 There does not appear to be a
linear relationship
OR N
B1 so test using pmcc not
appropriate [because that is for
linear relationships]
6 | (ii) | One-tail because evidence of a positive
relationship is sought | B1
[1] | 2.4 | E
o.e.6 Fig. 6 shows the wages earned in the last 12 months by each of a random sample of American males aged between 16 and 65 .
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{e6ee3a4a-3e76-4422-9a78-17b64b458f83-07_771_1278_340_392}
\captionsetup{labelformat=empty}
\caption{Fig. 6}
\end{center}
\end{figure}
A researcher wishes to test whether the sample provides evidence of a tendency for higher wages to be earned by older men in the age range 16 to 65 in America.\\
(i) The researcher needs to decide whether to use a test based on Pearson's product moment correlation coefficient or Spearman's rank correlation coefficient. Use the information in Fig. 6 to decide which test is more appropriate.\\
(ii) Should it be a one-tail or a two-tail test? Justify your answer.
\hfill \mbox{\textit{OCR MEI Further Statistics Major Q6 [3]}}