| Exam Board | OCR MEI |
|---|---|
| Module | Further Statistics Minor (Further Statistics Minor) |
| Year | 2019 |
| Session | June |
| Marks | 4 |
| 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 recall of basic statistical principles (census vs sample, bias in convenience sampling, and sample properties like representativeness). No calculations, mathematical techniques, or problem-solving are involved—just straightforward explanation of standard textbook concepts about sampling methods. |
| Spec | 2.01a Population and sample: terminology2.01c Sampling techniques: simple random, opportunity, etc2.01d Select/critique sampling: in context |
| Answer | Marks | Guidance |
|---|---|---|
| 3 | (a) | Because a census would involve destroying all of |
| the components. | E1 | |
| [1] | 2.3 | “Testing all items is expensive” |
| Answer | Marks |
|---|---|
| (b) | Because as more components are produced a |
| Answer | Marks | Guidance |
|---|---|---|
| It will not be representative of all the components. | E1 | |
| [1] | 2.2b | Only one reason needs to be |
| given | NB “The sample is too |
| Answer | Marks |
|---|---|
| (c) | The sample should be: |
| Answer | Marks |
|---|---|
| independently | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| [2] | 1.2 | |
| 1.2 | Any two reasons (B1 each) | NB “The sample needs |
Question 3:
3 | (a) | Because a census would involve destroying all of
the components. | E1
[1] | 2.3 | “Testing all items is expensive”
alone is E0
(b) | Because as more components are produced a
change might develop in the production process.
It is not a random method.
It will not be representative of all the components. | E1
[1] | 2.2b | Only one reason needs to be
given | NB “The sample is too
small” is E0
(c) | The sample should be:
unbiased
representative of the population
chosen so that components are selected
independently | B1
B1
[2] | 1.2
1.2 | Any two reasons (B1 each) | NB “The sample needs
to be large” is B03 A company has been commissioned to make 50 very expensive titanium components.\\
A sample of the components needs to be tested to ensure that they are sufficiently strong. However, this is a test to destruction, so the components which are tested can no longer be used.
\begin{enumerate}[label=(\alph*)]
\item Explain why it would not be appropriate to use a census in these circumstances.
A manager suggests that the first 5 components to be manufactured should be tested.
\item Explain why this would not be a sensible method of selecting the sample.
A statistician advises the manager that the sample selected should be a random sample.
\item Give two desirable features (other than randomness) that the sample should have.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Further Statistics Minor 2019 Q3 [4]}}