| Exam Board | CAIE |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2012 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Confidence intervals |
| Type | Calculate CI for proportion |
| Difficulty | Moderate -0.8 This is a straightforward confidence interval calculation for a proportion using the normal approximation, requiring only direct application of the standard formula with z = 2.326. The second part asks for a basic validity condition (e.g., np > 5 or random sampling), which is routine recall. Both parts are below average difficulty for A-level, involving no problem-solving or conceptual challenges. |
| Spec | 5.05c Hypothesis test: normal distribution for population mean5.05d Confidence intervals: using normal distribution |
| Answer | Marks | Guidance |
|---|---|---|
| \(p = \frac{18}{50}\) or \(0.36\) oe | B1 | |
| \(z = 2.326\) | B1 | |
| \(0.36 \pm z\sqrt{\frac{0.36 \times (1-0.36)}{50}}\) | M1 | Allow any \(z\) \((\neq 0\) or \(1)\) |
| \(= 0.202\) to \(0.518\) (3 sfs) | A1 [4] | Allow any brackets or none |
| Answer | Marks | Guidance |
|---|---|---|
| Sample random | B1 [1] | oe |
## Question 3:
**(i)**
$p = \frac{18}{50}$ or $0.36$ oe | B1 |
$z = 2.326$ | B1 |
$0.36 \pm z\sqrt{\frac{0.36 \times (1-0.36)}{50}}$ | M1 | Allow any $z$ $(\neq 0$ or $1)$
$= 0.202$ to $0.518$ (3 sfs) | A1 [4] | Allow any brackets or none
**(ii)**
Sample random | B1 [1] | oe
---3 In a sample of 50 students at Batlin college, 18 support the football club Real Madrid.\\
(i) Calculate an approximate $98 \%$ confidence interval for the proportion of students at Batlin college who support Real Madrid.\\
(ii) Give one condition for this to be a reliable result.
\hfill \mbox{\textit{CAIE S2 2012 Q3 [5]}}