| Exam Board | CAIE |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2023 |
| Session | June |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Combinations & Selection |
| Type | Critique of sampling methods |
| Difficulty | Easy -1.8 This is a straightforward question on simple random sampling that requires only basic understanding of reading random number tables and recognizing bias. Part (a) is pure pattern recognition (reading consecutive 3-digit numbers from the string), and part (b) tests whether students understand that overlapping selections create bias—a fundamental concept taught early in sampling methods with no calculation or problem-solving required. |
| Spec | 2.01c Sampling techniques: simple random, opportunity, etc |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| 180, 227 | B1 | One correct. Ignore incorrect numbers. |
| B1 | Both correct and no extra numbers seen. (Allow other correct use of list of digits). | |
| 2 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| These numbers are not independent of the previous numbers OR Only a finite number of digits used | B1 | Already used these numbers, so therefore not random. Does not include numbers not in the list, therefore not random (not random or biased needs a reason). |
| 1 |
## Question 2(a):
| Answer | Marks | Guidance |
|--------|-------|----------|
| 180, 227 | **B1** | One correct. Ignore incorrect numbers. |
| | **B1** | Both correct and no extra numbers seen. (Allow other correct use of list of digits). |
| | **2** | |
---
## Question 2(b):
| Answer | Marks | Guidance |
|--------|-------|----------|
| These numbers are not independent of the previous numbers **OR** Only a finite number of digits used | **B1** | Already used these numbers, so therefore not random. Does not include numbers not in the list, therefore not random (not random or biased needs a reason). |
| | **1** | |2 A club has 264 members, numbered from 1 to 264 . Donash wants to choose a random sample of members for a survey. In order to choose the members for the sample he uses his calculator to generate random digits. His first 20 random digits are as follows.
$$\begin{array} { l l l l }
10612 & 11801 & 21473 & 22759
\end{array}$$
\begin{enumerate}[label=(\alph*)]
\item The numbers of the first two members in the sample are 106 and 121.
Write down the numbers of the next two members in the sample.
\item To obtain the numbers for members after the 4th member, Donash starts with the second random digit, 0 , and obtains the numbers 061 and 211.
Explain why this method will not produce a random sample.
\end{enumerate}
\hfill \mbox{\textit{CAIE S2 2023 Q2 [3]}}