| Exam Board | AQA |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2007 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Chi-squared test of independence |
| Type | Standard 2×2 contingency table |
| Difficulty | Standard +0.3 This is a standard chi-squared test of independence with a 2×2 contingency table, requiring routine calculation of expected frequencies, test statistic, and comparison with critical value. While it involves multiple steps (10 marks), each step follows a well-rehearsed procedure with no conceptual challenges or novel problem-solving required, making it slightly easier than average. |
| Spec | 5.06a Chi-squared: contingency tables |
| \cline { 2 - 3 } \multicolumn{1}{c|}{} | Placebo | Drug |
| Condition improved | 20 | 46 |
| Condition did not improve | 55 | 29 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(H_0\): condition independent of treatment; \(H_1\): condition dependent upon treatment | B1 | |
| Totals: 66, 84, 75, 75 | B1 | |
| \(E_i\) attempted correctly | M1A1 | |
| Use of Yates' correction | M1 | |
| Final column completed | M1 | |
| \(\chi^2 = 16.91\) | A1 | Allow 16.9; if no Yates': possible M1A1M0M1A0; if 0.5 incorrectly used: possible M1A1M1M1A0 |
| \(\chi^2_{5\%}(1) = 3.841 < 16.91\) | \(B1\checkmark\) | For \(\chi^2\) on their \(\nu\) |
| Reject \(H_0\) | \(A1\checkmark\) | iff \(H_0\) stated correctly; dependent on third M1 |
| Evidence to suggest condition of patients may be dependent upon treatment received | \(E1\checkmark\) |
# Question 1:
| Answer/Working | Marks | Guidance |
|---|---|---|
| $H_0$: condition independent of treatment; $H_1$: condition dependent upon treatment | B1 | |
| Totals: 66, 84, 75, 75 | B1 | |
| $E_i$ attempted correctly | M1A1 | |
| Use of Yates' correction | M1 | |
| Final column completed | M1 | |
| $\chi^2 = 16.91$ | A1 | Allow 16.9; if no Yates': possible M1A1M0M1A0; if 0.5 incorrectly used: possible M1A1M1M1A0 |
| $\chi^2_{5\%}(1) = 3.841 < 16.91$ | $B1\checkmark$ | For $\chi^2$ on their $\nu$ |
| Reject $H_0$ | $A1\checkmark$ | iff $H_0$ stated correctly; dependent on third M1 |
| Evidence to suggest condition of patients may be dependent upon treatment received | $E1\checkmark$ | |
---1 Two groups of patients, suffering from the same medical condition, took part in a clinical trial of a new drug. One of the groups was given the drug whilst the other group was given a placebo, a drug that has no physical effect on their medical condition.
The table shows the number of patients in each group and whether or not their condition improved.
\begin{center}
\begin{tabular}{ | l | c | c | }
\cline { 2 - 3 }
\multicolumn{1}{c|}{} & Placebo & Drug \\
\hline
Condition improved & 20 & 46 \\
\hline
Condition did not improve & 55 & 29 \\
\hline
\end{tabular}
\end{center}
Conduct a $\chi ^ { 2 }$ test, at the $5 \%$ level of significance, to determine whether the condition of the patients at the conclusion of the trial is associated with the treatment that they were given.\\
(10 marks)
\hfill \mbox{\textit{AQA S2 2007 Q1 [10]}}