| Exam Board | AQA |
|---|---|
| Module | AS Paper 2 (AS Paper 2) |
| Year | 2023 |
| Session | June |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Hypothesis test of binomial distributions |
| Type | Interpret test conclusion or error |
| Difficulty | Easy -1.2 This is a straightforward hypothesis testing question requiring only standard recall of definitions. Part (a) asks for simple statement of H₀ and H₁ (routine bookwork), and part (b) asks for interpretation of a given result with no calculation needed. No problem-solving or novel application required—purely testing whether students know basic hypothesis test terminology and can write a contextual conclusion. |
| Spec | 2.05a Hypothesis testing language: null, alternative, p-value, significance2.05b Hypothesis test for binomial proportion |
| Answer | Marks |
|---|---|
| 18(a) | States both hypotheses |
| Answer | Marks | Guidance |
|---|---|---|
| = or µ = | 2.5 | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Subtotal | 1 | |
| Q | Marking instructions | AO |
| Answer | Marks |
|---|---|
| 18(b) | Infers that that the Null |
| Answer | Marks | Guidance |
|---|---|---|
| PI by wording of the conclusion | 2.2b | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| suggested | 3.2a | E1 |
| Subtotal | 2 | |
| Question 18 Total | 3 | |
| Q | Marking instructions | AO |
Question 18:
--- 18(a) ---
18(a) | States both hypotheses
correctly for a one-tailed test.
Accept equivalent in words.
Accept population proportion for
p.
Accept 25%, but not x = or x
= or µ = | 2.5 | B1 | H : p = 0.25
0
H : p > 0.25
1
Subtotal | 1
Q | Marking instructions | AO | Marks | Typical solution
--- 18(b) ---
18(b) | Infers that that the Null
Hypothesis is rejected
PI by wording of the conclusion | 2.2b | B1 | There is sufficient evidence to
suggest that the proportion of
customers buying a loaf of bread
has increased
Concludes correctly in context.
Must include ‘proportion’ OE,
not ‘probability’ or ‘number of’
‘Sufficient evidence’ OE
required.
Condone idea of causality if
suggested | 3.2a | E1
Subtotal | 2
Question 18 Total | 3
Q | Marking instructions | AO | Marks | Typical solutionIt is believed that 25% of the customers at a bakery buy a loaf of bread.
In an attempt to increase this proportion, the manager of the bakery provided free samples for the customers to taste.
To decide whether providing free samples had been effective, a large random sample of customers leaving the bakery were asked whether they had purchased a loaf of bread.
A hypothesis test at the 5% significance level was carried out on the data collected.
The test statistic calculated was found to be in the critical region.
\begin{enumerate}[label=(\alph*)]
\item State the Null and Alternative hypotheses for this test. [1 mark]
\item State, in context, the conclusion to this test. [2 marks]
\end{enumerate}
\hfill \mbox{\textit{AQA AS Paper 2 2023 Q18 [3]}}