| Exam Board | CAIE |
|---|---|
| Module | S2 (Statistics 2) |
| Session | Specimen |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Confidence intervals for population mean |
| Difficulty | Moderate -0.3 This is a straightforward two-part question requiring standard formulas for unbiased estimates and confidence intervals. Part (i) involves direct calculation using given summary statistics, and part (ii) applies the standard normal distribution formula for a confidence interval with known sample size (n=60, large enough for CLT). Both parts are routine applications of memorized procedures with no problem-solving or conceptual challenges beyond basic statistical literacy. |
| Spec | 5.05b Unbiased estimates: of population mean and variance5.05d Confidence intervals: using normal distribution |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(\frac{3420}{60}\ (= 57)\) | B1 | |
| \(\frac{60}{59}\left(\frac{195200}{60} - \text{'57'}^2\right)\) \((= 4.40678)\) | M1 | Oe |
| \(= 4.41\) (3 sf) | A1 | As final answer |
| Total | 3 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(\text{'57'} \pm z\sqrt{\frac{\text{'4.40678'}}{60}}\) | M1 | |
| \(z = 2.326\) | B1 | \(2.326 - 2.329\) (accept 2.33 if no better seen) |
| \([56.4 \text{ to } 57.6]\) (3 sf) | A1 | NB: use of biased variance in (ii) can score in full |
| Total | 3 |
## Question 3(i):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $\frac{3420}{60}\ (= 57)$ | B1 | |
| $\frac{60}{59}\left(\frac{195200}{60} - \text{'57'}^2\right)$ $(= 4.40678)$ | M1 | Oe |
| $= 4.41$ (3 sf) | A1 | As final answer |
| **Total** | **3** | |
---
## Question 3(ii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $\text{'57'} \pm z\sqrt{\frac{\text{'4.40678'}}{60}}$ | M1 | |
| $z = 2.326$ | B1 | $2.326 - 2.329$ (accept 2.33 if no better seen) |
| $[56.4 \text{ to } 57.6]$ (3 sf) | A1 | NB: use of biased variance in (ii) can score in full |
| **Total** | **3** | |
---3 Jagdeesh measured the lengths, $x$ minutes, of 60 randomly chosen lectures. His results are summarised below.\\
(i) Calculate unbiased estimates of the population mean and variance.\\
(ii) Calculate a $98 \%$ confidence interval for the population mean.\\
\hfill \mbox{\textit{CAIE S2 Q3 [6]}}