| Exam Board | CAIE |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2011 |
| 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. It requires only direct application of the standard formula with z=1.645, plus recognition that the normal approximation introduces error. The question involves minimal steps, no problem-solving insight, and is a standard textbook exercise below typical A-level difficulty. |
| Spec | 2.05a Hypothesis testing language: null, alternative, p-value, significance5.05d Confidence intervals: using normal distribution |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(\frac{\frac{18}{70}\times(1-\frac{18}{70})}{70} (= 0.00272886\ldots)\) | M1 | |
| \(z = 1.645\) | B1 | Seen |
| \(\frac{18}{70} \pm z \times \sqrt{0.00272886}\) | M1 | |
| \(0.171\) to \(0.343\) | A1[4] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Var (or sd) estimated, or \(N \sim B\) used | B1[1] |
## Question 2:
### Part (i):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $\frac{\frac{18}{70}\times(1-\frac{18}{70})}{70} (= 0.00272886\ldots)$ | M1 | |
| $z = 1.645$ | B1 | Seen |
| $\frac{18}{70} \pm z \times \sqrt{0.00272886}$ | M1 | |
| $0.171$ to $0.343$ | A1[4] | |
### Part (ii):
| Answer/Working | Marks | Guidance |
|---|---|---|
| Var (or sd) estimated, or $N \sim B$ used | B1[1] | |
---2 In a random sample of 70 bars of Luxcleanse soap, 18 were found to be undersized.\\
(i) Calculate an approximate $90 \%$ confidence interval for the proportion of all bars of Luxcleanse soap that are undersized.\\
(ii) Give a reason why your interval is only approximate.
\hfill \mbox{\textit{CAIE S2 2011 Q2 [5]}}