Standard +0.3 This is a straightforward chi-squared test of independence with expected frequencies already provided. Students only need to apply the standard χ² formula and compare to critical values - no calculation of expected frequencies or complex interpretation required. Slightly easier than average as the computational work is reduced.
7 Wade and Odelia are investigating whether there is an association between the region where a person lives and the brand of washing powder they use.
They decide to conduct a \(\chi ^ { 2 }\)-test for association and survey a random sample of 200 people.
The expected frequencies for the test have been calculated and are shown in the contingency table below.
States that there is an expected frequency less than 5
B1 (AO 1.1b)
e.g. "There is an expected frequency less than 5"
Explains how to refine model so that degrees of freedom for the test is 4; if specific rows are mentioned, must include North
E1 (AO 2.4)
e.g. Two rows have to be merged so that the degrees of freedom for the test is 4
Explains how to refine model so that degrees of freedom for the test is 3; if specific columns are mentioned, must include C
E1 (AO 2.4)
e.g. Or two columns have to be merged so that the degrees of freedom for the test is 3
Sub total: 3 marks
Question 7(b):
Answer
Marks
Guidance
Answer
Mark
Guidance
\(H_0\): There is no association between region and washing powder; \(H_1\): There is an association between region and washing powder
B1 (AO 2.5)
Both hypotheses using correct language OE; variables must be stated in at least the null hypothesis
\(\chi^2\) cv for 4 dof \(= 13.277\), or corresponding probability of test statistic AWRT 0.009
B1 (AO 1.1b)
Correct critical value AWRT 13.3
\(13.6 > 13.277\), therefore Reject \(H_0\)
R1 (AO 3.5a)
Evaluates \(\chi^2\) test statistic by correctly comparing critical value with test statistic or probability with 0.01
\(H_0\) rejected
E1F (AO 2.2b)
FT their comparison using a \(\chi^2\) model
Some evidence to suggest that there is an association between region and brand of washing powder used
E1F (AO 3.2a)
Concludes in context; conclusion must not be definite; FT their incorrect acceptance of \(H_0\) if stated or their comparison if not
Sub total: 5 marks
Question total: 8 marks
Paper total: 40 marks
## Question 7(a):
| Answer | Mark | Guidance |
|--------|------|----------|
| States that there is an expected frequency less than 5 | B1 (AO 1.1b) | e.g. "There is an expected frequency less than 5" |
| Explains how to refine model so that degrees of freedom for the test is 4; if specific rows are mentioned, must include North | E1 (AO 2.4) | e.g. Two rows have to be merged so that the degrees of freedom for the test is 4 |
| Explains how to refine model so that degrees of freedom for the test is 3; if specific columns are mentioned, must include C | E1 (AO 2.4) | e.g. Or two columns have to be merged so that the degrees of freedom for the test is 3 |
**Sub total: 3 marks**
---
## Question 7(b):
| Answer | Mark | Guidance |
|--------|------|----------|
| $H_0$: There is no association between region and washing powder; $H_1$: There is an association between region and washing powder | B1 (AO 2.5) | Both hypotheses using correct language **OE**; variables must be stated in at least the null hypothesis |
| $\chi^2$ cv for 4 dof $= 13.277$, or corresponding probability of test statistic **AWRT** 0.009 | B1 (AO 1.1b) | Correct critical value **AWRT** 13.3 |
| $13.6 > 13.277$, therefore Reject $H_0$ | R1 (AO 3.5a) | Evaluates $\chi^2$ test statistic by correctly comparing critical value with test statistic or probability with 0.01 |
| $H_0$ rejected | E1F (AO 2.2b) | **FT** their comparison using a $\chi^2$ model |
| Some evidence to suggest that there is an association between region and brand of washing powder used | E1F (AO 3.2a) | Concludes in context; conclusion must not be definite; **FT** their incorrect acceptance of $H_0$ if stated or their comparison if not |
**Sub total: 5 marks**
---
**Question total: 8 marks**
**Paper total: 40 marks**
7 Wade and Odelia are investigating whether there is an association between the region where a person lives and the brand of washing powder they use.
They decide to conduct a $\chi ^ { 2 }$-test for association and survey a random sample of 200 people.
The expected frequencies for the test have been calculated and are shown in the contingency table below.
\hfill \mbox{\textit{AQA Further AS Paper 2 Statistics 2022 Q7 [8]}}