| Exam Board | AQA |
|---|---|
| Module | AS Paper 2 (AS Paper 2) |
| Year | 2023 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Permutations & Arrangements |
| Type | Linear programming and optimization |
| Difficulty | Easy -1.8 This is a straightforward AS-level statistics question testing basic sampling terminology and methods. Part (a) requires describing simple random sampling (assign numbers, use random number generator) which is direct recall, and part (b) asks for stratified sampling as an alternative—both are standard textbook exercises with no problem-solving or mathematical calculation required. |
| Spec | 2.01c Sampling techniques: simple random, opportunity, etc |
| Answer | Marks |
|---|---|
| 14(a) | Sets up the numbering of the |
| Answer | Marks | Guidance |
|---|---|---|
| Allow 01 to 93 | 2.4 | E1 |
| Answer | Marks | Guidance |
|---|---|---|
| OE | 2.4 | E1 |
| Answer | Marks | Guidance |
|---|---|---|
| different employees/numbers | 2.4 | E1 |
| Answer | Marks | Guidance |
|---|---|---|
| Subtotal | 3 | |
| Q | Marking instructions | AO |
| Answer | Marks | Guidance |
|---|---|---|
| 14(b) | States either Stratified or Quota | 1.2 |
| Subtotal | 1 | |
| Question 14 Total | 4 | |
| Q | Marking instructions | AO |
Question 14:
--- 14(a) ---
14(a) | Sets up the numbering of the
population (allow 00 to 92)
Allow 01 to 93 | 2.4 | E1 | Number the employees from 1 to
93
Explains how the calculator
(random number generator) will
be used to generate random
numbers (two-digit PI by
between 1 and 93 or in this
range or ignore numbers out of
range or using these numbers)
If using random number tables
must state 2-digit numbers
OE | 2.4 | E1 | Choose random numbers from the
calculator in this range
Explains how to deal with
repeats (PI) and identify 20
different employees/numbers | 2.4 | E1 | Ignore repeats and continue until
20 different employees have been
selected
Subtotal | 3
Q | Marking instructions | AO | Marks | Typical solution
--- 14(b) ---
14(b) | States either Stratified or Quota | 1.2 | B1 | Stratified sampling
Subtotal | 1
Question 14 Total | 4
Q | Marking instructions | AO | Marks | Typical solutionThe manager of a factory wants to introduce a bonus scheme.
The factory has 65 employees who work in production and 28 employees who work in the office.
The manager decides to collect the opinions of a sample of these 93 employees.
\begin{enumerate}[label=(\alph*)]
\item Explain how the manager could collect a simple random sample of 20 employees. [3 marks]
\item The manager collected a simple random sample of 20 employees.
The manager noticed that all 20 of the employees in the sample worked in production and therefore the sample was not representative.
State a different method of sampling that would give a representative sample. [1 mark]
\end{enumerate}
\hfill \mbox{\textit{AQA AS Paper 2 2023 Q14 [4]}}