| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2008 |
| Session | June |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Chi-squared test of independence |
| Type | Standard 2×3 contingency table |
| Difficulty | Standard +0.3 This is a standard chi-squared test of independence with a 2×3 contingency table. Students must calculate expected frequencies, compute the test statistic, and compare to critical values—all routine S3 procedures with no conceptual challenges beyond textbook application. |
| Spec | 5.06a Chi-squared: contingency tables |
| \cline { 3 - 4 } \multicolumn{2}{c|}{} | Course | |||
| \cline { 3 - 5 } \multicolumn{2}{c|}{} | Arts | Science | Humanities | |
| Esuder | Boy | 30 | 50 | 35 |
| \cline { 2 - 5 } | Girl | 40 | 20 | 42 |
| Answer | Marks | Guidance |
|---|---|---|
| \(\frac{115 \times 70}{217} = 37.0967...\) or \(\frac{1150}{31}\) (etc) \(\frac{1265}{31}\), \(\frac{1020}{31}\), \(\frac{1122}{31}\) | M1 | |
| Expected (Obs) | A | S |
| Boy | 37.1 (30) | 37.1 (50) |
| Girl | 32.9 (40) | 32.9 (20) |
| A1A1 | ||
| \(H_0\): There is no association between course and gender | B1 | |
| \(H_1\): There is some association between course and gender (both) | B1 | |
| \(\sum \frac{(O-E)^2}{E} = \frac{(37.1-30)^2}{37.1} + \frac{(32.9-40)^2}{32.9} + ... + \frac{(36.2-42)^2}{36.2}\) | M1A1ft | |
| \(= 1.358 + 4.485 + 0.824 + 1.532 + 5.058 + 0.929 = 14.189...\) | A1 | awrt 14.2 |
| \(\nu = (3-1)(2-1) = 2\), \(\chi_2^2(1\%)\) critical value is 9.210 | B1, B1ft | (condone 9.21) |
| Significant result or reject null hypothesis | M1 | |
| There is evidence of an association between course taken and gender | A1ft | (11 marks) |
$\frac{115 \times 70}{217} = 37.0967...$ or $\frac{1150}{31}$ (etc) $\frac{1265}{31}$, $\frac{1020}{31}$, $\frac{1122}{31}$ | M1 |
| **Expected (Obs)** | **A** | **S** | **H** |
|---|---|---|---|
| **Boy** | 37.1 (30) | 37.1 (50) | 40.8 (35) |
| **Girl** | 32.9 (40) | 32.9 (20) | 36.2 (42) |
| A1A1 |
$H_0$: There is no association between course and gender | B1 |
$H_1$: There is some association between course and gender (both) | B1 |
$\sum \frac{(O-E)^2}{E} = \frac{(37.1-30)^2}{37.1} + \frac{(32.9-40)^2}{32.9} + ... + \frac{(36.2-42)^2}{36.2}$ | M1A1ft |
$= 1.358 + 4.485 + 0.824 + 1.532 + 5.058 + 0.929 = 14.189...$ | A1 | awrt 14.2
$\nu = (3-1)(2-1) = 2$, $\chi_2^2(1\%)$ critical value is 9.210 | B1, B1ft | (condone 9.21)
Significant result or reject null hypothesis | M1 |
There is evidence of an association between course taken and gender | A1ft | (11 marks)
**[Correct answers only score full marks]**
---2. Students in a mixed sixth form college are classified as taking courses in either Arts, Science or Humanities. A random sample of students from the college gave the following results
\begin{center}
\begin{tabular}{ | c | c | c | c | c | }
\cline { 3 - 4 }
\multicolumn{2}{c|}{} & \multicolumn{3}{c|}{Course} \\
\cline { 3 - 5 }
\multicolumn{2}{c|}{} & Arts & Science & Humanities \\
\hline
Esuder & Boy & 30 & 50 & 35 \\
\cline { 2 - 5 }
& Girl & 40 & 20 & 42 \\
\hline
\end{tabular}
\end{center}
Showing your working clearly, test, at the $1 \%$ level of significance, whether or not there is an association between gender and the type of course taken. State your hypotheses clearly.\\
\hfill \mbox{\textit{Edexcel S3 2008 Q2 [11]}}