| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2006 |
| 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 application with a 3×2 contingency table. Students must state hypotheses, calculate expected frequencies, compute the test statistic, find critical value with 2 degrees of freedom, and conclude. While it requires multiple steps and careful calculation, it follows a completely routine procedure taught explicitly in S3 with no novel problem-solving or insight required, making it slightly easier than average. |
| Spec | 5.06a Chi-squared: contingency tables |
| Age in years | Red | Blue | Totals |
| 4 | 12 | 6 | 18 |
| 8 | 10 | 7 | 17 |
| 12 | 6 | 9 | 15 |
| Totals | 28 | 22 | 50 |
| Answer | Marks | Guidance |
|---|---|---|
| \(H_0\): No association between age and colour (independent) | B1 | |
| \(H_1\): Association between age and colour (Not independent) | B1 | |
| O | E | \(\frac{(O-E)^2}{E}\) |
| 12 | 10.08 | 0.3657... |
| 6 | 7.92 | 0.4654... |
| 10 | 9.52 | 0.2242... |
| 7 | 7.48 | 0.0308... |
| 6 | 5.4 | 0.6657... |
| 9 | 6.6 | 0.5727... |
| M1A1 | Attacher BTACE \(\frac{(O-E)^2}{(O-E)^2}\) | |
| \(\sum \frac{(O-E)^2}{E} = 2.4461...\) | awrt \(\sum 2.44\) M1A1 | (must 2.44 shown) |
| \(\nu = (3-1)(2-1) = 2\), \(\mu_c^2 = 5.991\) | B1 B1N | |
| Insufficient evidence to reject \(H_0\). No association between age and colour | A1N | (11) |
| (cv for correct h/s for H) | TOTAL 11 |
## Part (a)
$H_0$: No association between age and colour (independent) | B1 |
$H_1$: Association between age and colour (Not independent) | B1 |
| O | E | $\frac{(O-E)^2}{E}$ |
|---|---|---|
| 12 | 10.08 | 0.3657... |
| 6 | 7.92 | 0.4654... |
| 10 | 9.52 | 0.2242... |
| 7 | 7.48 | 0.0308... |
| 6 | 5.4 | 0.6657... |
| 9 | 6.6 | 0.5727... |
| M1A1 | Attacher BTACE $\frac{(O-E)^2}{(O-E)^2}$
$\sum \frac{(O-E)^2}{E} = 2.4461...$ | awrt $\sum 2.44$ M1A1 | (must 2.44 shown)
$\nu = (3-1)(2-1) = 2$, $\mu_c^2 = 5.991$ | B1 B1N |
Insufficient evidence to reject $H_0$. No association between age and colour | A1N | (11)
(cv for correct h/s for H) | | TOTAL 11
---A research worker studying colour preference and the age of a random sample of 50 children obtained the results shown below.
\begin{center}
\begin{tabular}{|c|c|c|c|}
\hline
Age in years & Red & Blue & Totals \\
\hline
4 & 12 & 6 & 18 \\
8 & 10 & 7 & 17 \\
12 & 6 & 9 & 15 \\
\hline
Totals & 28 & 22 & 50 \\
\hline
\end{tabular}
\end{center}
Using a 5\% significance level, carry out a test to decide whether or not there is an association between age and colour preference. State your hypotheses clearly. [11]
\hfill \mbox{\textit{Edexcel S3 2006 Q6 [11]}}