| Exam Board | CAIE |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2016 |
| Session | November |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Combinations & Selection |
| Type | Implementing simple random or systematic sampling |
| Difficulty | Easy -1.8 This is a straightforward question on random sampling procedures requiring only basic arithmetic (multiplication and rounding) and simple conceptual understanding of sampling with replacement. Part (i) is pure calculation, part (ii) requires working backwards with simple inequalities, and part (iii) tests basic awareness that duplicates can occur. No problem-solving or statistical theory required. |
| Spec | 2.01c Sampling techniques: simple random, opportunity, etc2.01d Select/critique sampling: in context |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| 59 | B1 | [1] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Any \(x\) such that \(0.687 \leqslant x \leqslant 0.693\) (3 sf) | B1 | [1] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Possible repeats | B1 | [1] |
## Question 2:
### Part (i):
| Answer/Working | Marks | Guidance |
|---|---|---|
| 59 | B1 | [1] |
### Part (ii):
| Answer/Working | Marks | Guidance |
|---|---|---|
| Any $x$ such that $0.687 \leqslant x \leqslant 0.693$ (3 sf) | B1 | [1] | or 0.69 or "…$0.686$.. $< 0.693$ rec" |
### Part (iii):
| Answer/Working | Marks | Guidance |
|---|---|---|
| Possible repeats | B1 | [1] |
---2 Dominic wishes to choose a random sample of five students from the 150 students in his year. He numbers the students from 1 to 150 . Then he uses his calculator to generate five random numbers between 0 and 1 . He multiplies each random number by 150 and rounds up to the next whole number to give a student number.\\
(i) Dominic's first random number is 0.392 . Find the student number that is produced by this random number.\\
(ii) Dominic's second student number is 104 . Find a possible random number that would produce this student number.\\
(iii) Explain briefly why five random numbers may not be enough to produce a sample of five student numbers.
\hfill \mbox{\textit{CAIE S2 2016 Q2 [3]}}