| Exam Board | CAIE |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2024 |
| Session | March |
| 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 requiring standard formula application (sample proportion ± z-critical value × standard error) followed by a simple comparison interpretation. The mechanics are routine for S2 level with no conceptual subtlety—students just need to check if 0.40 lies within their interval. Easier than average A-level statistics. |
| Spec | 5.05d Confidence intervals: using normal distribution |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(\frac{78}{250} \pm z \times \sqrt{\frac{\frac{78}{250}\times\left(1-\frac{78}{250}\right)}{250}}\) | M1 | Use of a correct formula (any \(z\)) |
| \(z = 2.326\) | B1 | |
| \(= 0.244\) to \(0.380\) (3 sf) | A1 | Must be an interval |
| 3 |
| Answer | Marks | Guidance |
|---|---|---|
| Unlikely to be true because confidence interval does not contain 0.4 | B1 ft | FT their confidence interval. Must include reason and 'unlikely'. Allow "not true because 0.4 is not in the confidence interval." Note: "CI only goes up to 0.38 so not true" and "'it' lies outside the CI" both score B0. |
## Question 2:
**Part (a):**
| Answer | Marks | Guidance |
|--------|-------|----------|
| $\frac{78}{250} \pm z \times \sqrt{\frac{\frac{78}{250}\times\left(1-\frac{78}{250}\right)}{250}}$ | **M1** | Use of a correct formula (any $z$) |
| $z = 2.326$ | **B1** | |
| $= 0.244$ to $0.380$ (3 sf) | **A1** | Must be an interval |
| | **3** | |
## Question 2(b):
| Unlikely to be true because confidence interval does not contain 0.4 | B1 ft | FT their confidence interval. Must include reason and 'unlikely'. Allow "not true because 0.4 is not in the confidence interval." Note: "CI only goes up to 0.38 so not true" and "'it' lies outside the CI" both score B0. |
---2 A random sample of 250 people living in Barapet was chosen. It was found that 78 of these people owned a BETEC phone.
\begin{enumerate}[label=(\alph*)]
\item Calculate an approximate $98 \%$ confidence interval for the proportion of people living in Barapet who own a BETEC phone.
\item Manjit claims that more than $40 \%$ of the people living in Barapet own a BETEC phone.
Use your answer to part (a) to comment on this claim.
\end{enumerate}
\hfill \mbox{\textit{CAIE S2 2024 Q2 [4]}}