| Exam Board | CAIE |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2010 |
| Session | November |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Combinations & Selection |
| Type | Critique of sampling methods |
| Difficulty | Easy -1.8 This is a straightforward question testing basic understanding of sampling methods. Part (i) requires simple recall of why voluntary response sampling is biased (self-selection, non-response). Part (ii) is a mechanical exercise in reading random number tables with no problem-solving required—students just need to identify which 4-digit groups fall within 1-7302. |
| Spec | 2.01c Sampling techniques: simple random, opportunity, etc |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Only the more committed, or less busy etc | B1 | Any sensible category of readers who will not respond implied |
| Only readers of that particular issue | B1 [2] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Three randomly generated 4-digit numbers given | B1 | Starting with 4975 |
| 4975, 3952, (0)386 | B1dep [2] | Accept 4975 0239 5203 and 4975 5203 6088. SC alternative consistent methods producing a set of 3 randomly generated 4-digit numbers can score B1 for the first number and B1dep for all three numbers, all \(\leq\) 7302 |
## Question 2:
### Part (i):
| Answer/Working | Marks | Guidance |
|---|---|---|
| Only the more committed, or less busy etc | B1 | Any sensible category of readers who will not respond implied |
| Only readers of that particular issue | B1 [2] | |
### Part (ii):
| Answer/Working | Marks | Guidance |
|---|---|---|
| Three randomly generated 4-digit numbers given | B1 | Starting with 4975 |
| 4975, 3952, (0)386 | B1dep [2] | Accept 4975 0239 5203 and 4975 5203 6088. SC alternative consistent methods producing a set of 3 randomly generated 4-digit numbers can score B1 for the first number and B1dep for all three numbers, all $\leq$ 7302 |
---2 The editor of a magazine wishes to obtain the views of a random sample of readers about the future of the magazine.\\
(i) A sub-editor proposes that they include in one issue of the magazine a questionnaire for readers to complete and return. Give two reasons why the readers who return the questionnaire would not form a random sample.
The editor decides to use a table of random numbers to select a random sample of 50 readers from the 7302 regular readers. These regular readers are numbered from 1 to 7302 . The first few random numbers which the editor obtains from the table are as follows.
$$49757 \quad 80239 \quad 52038 \quad 60882$$
(ii) Use these random numbers to select the first three members in the sample.
\hfill \mbox{\textit{CAIE S2 2010 Q2 [4]}}