Standard +0.3 This is a standard chi-squared test of independence with a 2×2 or 2×3 contingency table. While it's a Further Maths topic (making it slightly above average), it's a routine application requiring calculation of expected frequencies, the test statistic, and comparison with critical values—all standard procedures with no novel insight required.
7 Mohammed is conducting a medical trial to study the effect of two drugs, \(A\) and \(B\), on the amount of time it takes to recover from a particular illness.
Drug \(A\) is used by one group of 60 patients and drug \(B\) is used by a second group of 60 patients.
The results are summarised in the table:
Calculates \(\chi^2\) test statistic correctly AWRT 3 s.f.; condone 9.52
\(\chi^2\) cv for 2 df \(= 9.210\) (\(p=0.0085\))
B1F
States critical value (or \(p\)-value); follow through their \(\chi^2\) value; if columns merged follow through 6.635 for 1 dof
\(9.53 > 9.210\)
M1
Evaluates \(\chi^2\) test statistic by comparing cv with ts (or \(p\)-value with 0.01)
Reject \(H_0\)
R1
Infers \(H_0\) rejected, follow through with their ts and cv
Some evidence to suggest/support that recovery time and drug used are not independent / Mohammed's claim is correct
E1
Concludes in context based on their hypotheses (not definite); consistent with decision; can be awarded if seen in part (b)
Question 7(b):
Answer
Marks
Guidance
Answer/Working
Mark
Guidance
Largest sources of association: Drug A/3 weeks and Drug B/3 weeks; \(\frac{(O-E)^2}{E}=2.5\)
E1
Considers \(\frac{(O-E)^2}{E}\) to identify largest sources as Drug A or B/3 weeks; OR considers \((O-E)\) to identify largest sources as Drug A or B/1 week; do not allow if no reference to why source selected
Fewer people than expected using Drug A have a recovery time of 3 weeks, or more people than expected using Drug B have a recovery time of 3 weeks
E1
Interprets main source of association in context; condone multiple comments if not contradictory
## Question 7(a):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $H_0$: There is no association between recovery time and drug used; $H_1$: There is an association between recovery time and drug used | B1 | States both hypotheses using correct language; variables must be included in at least null hypothesis |
| Expected values: A: 28.5, 21.5, 10; B: 28.5, 21.5, 10 | M1 | Calculates at least four correct expected values (PI); allow even if columns merged |
| $\sum\frac{(O-E)^2}{E} = \frac{(36-28.5)^2}{28.5}+\frac{(19-21.5)^2}{21.5}+\frac{(5-10)^2}{10}+\frac{(21-28.5)^2}{28.5}+\frac{(24-21.5)^2}{21.5}+\frac{(15-10)^2}{10} = 9.53$ | A1 | Calculates $\chi^2$ test statistic correctly AWRT 3 s.f.; condone 9.52 |
| $\chi^2$ cv for 2 df $= 9.210$ ($p=0.0085$) | B1F | States critical value (or $p$-value); follow through their $\chi^2$ value; if columns merged follow through 6.635 for 1 dof |
| $9.53 > 9.210$ | M1 | Evaluates $\chi^2$ test statistic by comparing cv with ts (or $p$-value with 0.01) |
| Reject $H_0$ | R1 | Infers $H_0$ rejected, follow through with their ts and cv |
| Some evidence to suggest/support that recovery time and drug used are not independent / Mohammed's claim is correct | E1 | Concludes in context based on their hypotheses (not definite); consistent with decision; can be awarded if seen in part (b) |
## Question 7(b):
| Answer/Working | Mark | Guidance |
|---|---|---|
| Largest sources of association: Drug A/3 weeks and Drug B/3 weeks; $\frac{(O-E)^2}{E}=2.5$ | E1 | Considers $\frac{(O-E)^2}{E}$ to identify largest sources as Drug A or B/3 weeks; OR considers $(O-E)$ to identify largest sources as Drug A or B/1 week; do not allow if no reference to why source selected |
| Fewer people than expected using Drug A have a recovery time of 3 weeks, or more people than expected using Drug B have a recovery time of 3 weeks | E1 | Interprets main source of association in context; condone multiple comments if not contradictory |
7 Mohammed is conducting a medical trial to study the effect of two drugs, $A$ and $B$, on the amount of time it takes to recover from a particular illness.
Drug $A$ is used by one group of 60 patients and drug $B$ is used by a second group of 60 patients.
The results are summarised in the table:
\hfill \mbox{\textit{AQA Further AS Paper 2 Statistics 2019 Q7 [9]}}