| Exam Board | CAIE |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2018 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Confidence intervals |
| Type | Calculate CI for proportion |
| Difficulty | Moderate -0.3 This is a straightforward application of the standard confidence interval formula for a proportion with a large sample (n=100). Part (i) requires substituting values into a formula students should know, and part (ii) is a simple interpretation comparing the interval to 1/6. The non-standard confidence level (94%) adds minimal difficulty as students just need to find the correct z-value. |
| Spec | 2.04d Normal approximation to binomial5.05d Confidence intervals: using normal distribution |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(\frac{20}{100} \pm z \times \sqrt{\frac{0.2 \times (1-0.2)}{100}}\) | M1 | Any \(z\) |
| \(z = 1.881\) or \(1.882\) | B1 | |
| \(= 0.125\) to \(0.275\) | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(\frac{1}{6}\) is within this range; No evidence of bias concerning 2 | B1ft | Both statements needed |
**Question 2(i):**
| Answer | Marks | Guidance |
|--------|-------|----------|
| $\frac{20}{100} \pm z \times \sqrt{\frac{0.2 \times (1-0.2)}{100}}$ | M1 | Any $z$ |
| $z = 1.881$ or $1.882$ | B1 | |
| $= 0.125$ to $0.275$ | A1 | |
**Question 2(ii):**
| Answer | Marks | Guidance |
|--------|-------|----------|
| $\frac{1}{6}$ is within this range; No evidence of bias concerning 2 | B1ft | Both statements needed |
---2 A six-sided die is suspected of bias. The die is thrown 100 times and it is found that the score is 2 on 20 throws. It is given that the probability of obtaining a score of 2 on any throw is $p$.\\
(i) Find an approximate $94 \%$ confidence interval for $p$.\\
(ii) Use your answer to part (i) to comment on whether the die may be biased.\\
\hfill \mbox{\textit{CAIE S2 2018 Q2 [4]}}