| Exam Board | AQA |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2008 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Chi-squared test of independence |
| Type | Interpret association after test |
| 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. The setup is straightforward with clear data, though it requires careful execution of multiple steps and interpretation of results. |
| Spec | 5.06a Chi-squared: contingency tables |
| \cline { 2 - 4 } \multicolumn{1}{c|}{} | Asthma | No asthma | Total |
| Heavy traffic | 52 | 58 | 110 |
| Light traffic | 28 | 62 | 90 |
| Total | 80 | 120 | 200 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(E_i\) attempted | M1 | E attempted |
| \(\ | O_i - E_i\ | - 0.5\) calculated |
| \(\chi^2 = \sum\frac{( | O_i-E_i | -0.5)^2}{E_i}\) attempted; values: 1.2784, 0.8523, 1.5625, 1.0417 giving total 4.7349 |
| \(H_0\): No association between incidence of asthma and volume of traffic; \(H_1\): Association | B1 | At least \(H_0\) stated correctly |
| \(\nu = 1\); \(\chi^2_{\text{crit}} = 3.841 < 4.7349\) | B1 | Critical value |
| Reject \(H_0\) at 5% level | A1ft | |
| Evidence to suggest an association between the incidence of asthma in children and the volume of traffic where they live | E1ft | 8 marks total |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| More than expected had asthma | E1 | 1 mark; dep on statement of association |
## Question 1:
### Part (a)
| Answer/Working | Marks | Guidance |
|---|---|---|
| $E_i$ attempted | M1 | E attempted |
| $\|O_i - E_i\| - 0.5$ calculated | M1 | Yates' correction attempted |
| $\chi^2 = \sum\frac{(|O_i-E_i|-0.5)^2}{E_i}$ attempted; values: 1.2784, 0.8523, 1.5625, 1.0417 giving total 4.7349 | M1, A1 | AWFW 4.73 to 4.74 |
| $H_0$: No association between incidence of asthma and volume of traffic; $H_1$: Association | B1 | At least $H_0$ stated correctly |
| $\nu = 1$; $\chi^2_{\text{crit}} = 3.841 < 4.7349$ | B1 | Critical value |
| Reject $H_0$ at 5% level | A1ft | |
| Evidence to suggest an association between the incidence of asthma in children and the volume of traffic where they live | E1ft | 8 marks total |
### Part (b)
| Answer/Working | Marks | Guidance |
|---|---|---|
| More than expected had asthma | E1 | 1 mark; dep on statement of association |
---1 It is thought that the incidence of asthma in children is associated with the volume of traffic in the area where they live.
Two surveys of children were conducted: one in an area where the volume of traffic was heavy and the other in an area where the volume of traffic was light.
For each area, the table shows the number of children in the survey who had asthma and the number who did not have asthma.
\begin{center}
\begin{tabular}{ | l | c | c | c | }
\cline { 2 - 4 }
\multicolumn{1}{c|}{} & Asthma & No asthma & Total \\
\hline
Heavy traffic & 52 & 58 & 110 \\
\hline
Light traffic & 28 & 62 & 90 \\
\hline
Total & 80 & 120 & 200 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Use a $\chi ^ { 2 }$ test, at the $5 \%$ level of significance, to determine whether the incidence of asthma in children is associated with the volume of traffic in the area where they live.
\item Comment on the number of children in the survey who had asthma, given that they lived in an area where the volume of traffic was heavy.
\end{enumerate}
\hfill \mbox{\textit{AQA S2 2008 Q1 [9]}}