| Exam Board | AQA |
|---|---|
| Module | Further AS Paper 2 Statistics (Further AS Paper 2 Statistics) |
| Year | 2020 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Chi-squared test of independence |
| Type | Test statistic given, complete the test |
| Difficulty | Moderate -0.8 This is a straightforward chi-squared test interpretation question requiring only standard recall of hypotheses, critical value comparison, and conclusion statement. Part (b) involves looking up a critical value and comparing 44.1 to it—purely mechanical with no problem-solving. The context is standard A-level statistics with no novel insight required, making it easier than average despite being Further Maths content. |
| Spec | 5.06a Chi-squared: contingency tables |
| Answer | Marks | Guidance |
|---|---|---|
| 7(a) | States both hypotheses using | |
| correct language. | 2.5 | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| 7(b) | Obtains the correct critical value | |
| (43.773) or p-value (0.0467). | 1.1b | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| p-value with 0.05). | 3.5a | R1 |
| Answer | Marks | Guidance |
|---|---|---|
| FT their comparison. | 2.2b | E1 |
| Answer | Marks | Guidance |
|---|---|---|
| FT their comparison | 2.1 | E1 |
| Answer | Marks |
|---|---|
| 7(c) | States their conclusion to the |
| Answer | Marks | Guidance |
|---|---|---|
| conclusion in 7(b). | 3.2a | E1 |
| Answer | Marks | Guidance |
|---|---|---|
| Total | 6 | |
| Q | Marking Instructions | AO |
Question 7:
--- 7(a) ---
7(a) | States both hypotheses using
correct language. | 2.5 | B1 | H : There is no association
0
between meal ordered and age of
customer.
H : There is an association
1
between meal ordered and age of
customer.
--- 7(b) ---
7(b) | Obtains the correct critical value
(43.773) or p-value (0.0467). | 1.1b | B1 | χ2 cv for 30 df = 43.773
44.1 > 43.773
Reject H
0
Sylvia was not correct to accept the
null hypothesis.
Evaluates the χ2-test statistic by
correctly comparing their critical
value with the test statistic (or their
p-value with 0.05). | 3.5a | R1
Infers H rejected.
0
FT their comparison. | 2.2b | E1
Concludes that Sylvia was not
correct to accept the null
hypothesis.
FT their comparison | 2.1 | E1
--- 7(c) ---
7(c) | States their conclusion to the
hypothesis test in context.
(Conclusion must not be definite)
FT their null and alternative
hypotheses in 7(a) and their
conclusion in 7(b). | 3.2a | E1 | Significant evidence to suggest that
there is an association between
meal ordered and gender of
customer.
Total | 6
Q | Marking Instructions | AO | Marks | Typical SolutionA restaurant has asked Sylvia to conduct a $\chi^2$ test for association between meal ordered and age of customer.
\begin{enumerate}[label=(\alph*)]
\item State the hypotheses that Sylvia should use for her test.
[1 mark]
\item Sylvia correctly calculates her value of the test statistic to be 44.1
She uses a 5% level of significance and the degrees of freedom for the test is 30
Sylvia accepts the null hypothesis.
Explain whether or not Sylvia was correct to accept the null hypothesis.
[4 marks]
\item State in context the correct conclusion to Sylvia's test.
[1 mark]
\end{enumerate}
\hfill \mbox{\textit{AQA Further AS Paper 2 Statistics 2020 Q7 [6]}}