| Exam Board | CAIE |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2017 |
| Session | June |
| Marks | 4 |
| 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 question for a proportion using normal approximation. Part (i) requires standard application of the formula with given confidence level and sample data. Part (ii) is direct recall of confidence interval interpretation. Both parts are routine with no problem-solving or conceptual challenges beyond basic understanding. |
| Spec | 2.05a Hypothesis testing language: null, alternative, p-value, significance |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(z = 1.751\) | B1 | |
| \(\frac{103}{200} \pm z\sqrt{\frac{\frac{103}{200}\times(1-\frac{103}{200})}{200}}\) | M1 | All correct except for recognisable value of \(z\); allow for one side only |
| \(= 0.453\) to \(0.577\) (3 sf) as final answer | A1 | Must be an interval |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(0.08\) or \(8\%\), \(8/100\) | B1 |
## Question 2(i):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $z = 1.751$ | B1 | |
| $\frac{103}{200} \pm z\sqrt{\frac{\frac{103}{200}\times(1-\frac{103}{200})}{200}}$ | M1 | All correct except for recognisable value of $z$; allow for one side only |
| $= 0.453$ to $0.577$ (3 sf) as final answer | A1 | Must be an interval |
---
## Question 2(ii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $0.08$ or $8\%$, $8/100$ | B1 | |
---2 In a random sample of 200 shareholders of a company, 103 said that they wanted a change in the management.\\
(i) Find an approximate $92 \%$ confidence interval for the proportion, $p$, of all shareholders who want a change in the management.\\
(ii) State the probability that a $92 \%$ confidence interval does not contain $p$.\\
\hfill \mbox{\textit{CAIE S2 2017 Q2 [4]}}