| Exam Board | OCR MEI |
|---|---|
| Module | Further Statistics Minor (Further Statistics Minor) |
| Year | 2023 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Combinations & Selection |
| Type | Critique of sampling methods |
| Difficulty | Easy -1.8 This is a purely conceptual question about sampling methodology requiring only common-sense reasoning about practical considerations (cost vs. reliability, bias from non-random sampling). No mathematical calculation or statistical theory is needed—students simply explain why sample sizes might be too small/large and why sampling methods should be random and representative. This is significantly easier than typical A-level questions that require actual problem-solving or calculation. |
| Spec | 2.01a Population and sample: terminology2.01c Sampling techniques: simple random, opportunity, etc2.01d Select/critique sampling: in context |
| Answer | Marks | Guidance |
|---|---|---|
| 2 | (a) | (i) |
| Answer | Marks | Guidance |
|---|---|---|
| unlikely to be close to the population parameters | E1 | |
| [1] | 2.4 | E0 if comment only refers to the sample being too small. |
| Answer | Marks | Guidance |
|---|---|---|
| 2 | (a) | (ii) |
| Answer | Marks | Guidance |
|---|---|---|
| useful information (about the strength) | E1 | |
| [1] | 2.4 | E0 if comment only refers to the sample being too large. |
| Answer | Marks | Guidance |
|---|---|---|
| 2 | (b) | For example, one of: |
| Answer | Marks | Guidance |
|---|---|---|
| (about the population) | E1 | |
| [1] | 2.2b | Allow any suitable answer |
| 2 | (c) | The sample should be: |
| Answer | Marks | Guidance |
|---|---|---|
| • random | B1 B1 | |
| [2] | 1.2 | Any two from these three |
Question 2:
2 | (a) | (i) | For example, one of:
• a sample this small might not give any useful
information (about the strength)
• a sample this small is unlikely to be representative
of the population
• the sample statistics from such a small sample are
unlikely to be close to the population parameters | E1
[1] | 2.4 | E0 if comment only refers to the sample being too small.
Allow any suitable answer
2 | (a) | (ii) | For example, one of:
• it is wasteful as the cans cannot then be used/it is
a test to destruction
• a (far) smaller sample size is adequate to give
useful information (about the strength) | E1
[1] | 2.4 | E0 if comment only refers to the sample being too large.
Allow any suitable answer
2 | (b) | For example, one of:
• there may have been a fault earlier in the batch
which then corrected itself for the later tins
• if there has been a fault throughout the batch it is
not sensible to only discover that at the end
• this would not be random so it would not be
appropriate to make (statistical) inferences
(about the population) | E1
[1] | 2.2b | Allow any suitable answer
2 | (c) | The sample should be:
• unbiased
• representative of the population
• random | B1 B1
[2] | 1.2 | Any two from these three2 A company manufactures batches of twenty thousand tins which are subsequently filled with fruit. The company tests tins from each batch to make sure that they are strong enough. The test is easy and cheap to carry out, but when a tin has been tested it is no longer suitable for filling with fruit.
\begin{enumerate}[label=(\alph*)]
\item \begin{enumerate}[label=(\roman*)]
\item Explain why a sample size of 5 tins per batch may not be appropriate in this case.
\item Explain why a sample size of 1000 tins per batch may not be appropriate in this case.
The company tests a sample of 30 tins from each batch.
\end{enumerate}\item Explain why it would not be sensible for the sample to consist of the final 30 tins produced in a batch.
\item Give two features that the sample should have.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Further Statistics Minor 2023 Q2 [5]}}