| Exam Board | CAIE |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2016 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Confidence intervals |
| Type | Recover sample stats from CI |
| Difficulty | Moderate -0.8 This is a straightforward confidence interval question requiring only recall of standard formulas: the sample proportion is the midpoint of the interval, and the confidence level comes from solving z × SE = width/2. Both parts are routine calculations with no conceptual difficulty or problem-solving required. |
| Spec | 5.05d Confidence intervals: using normal distribution |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(((0.5672 + 0.6528) \div 2) = 0.61\) | B1 [1] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(`0.61` + z\sqrt{\frac{`0.61` \times (1-`0.61`)}{350}} = 0.6528\) | M1 | oe |
| \(z = 0.0428 \times \sqrt{\frac{700}{`0.61` \times (1-`0.61`)}}\) oe | M1 | correct rearrangement of correct equation, ft '0.61' |
| \(= 2.321\) | A1 | |
| 98% confidence | A1ft [4] | ft their \(z\) (dep on both Ms) |
## Question 3:
### Part (i):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $((0.5672 + 0.6528) \div 2) = 0.61$ | B1 [1] | |
### Part (ii):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $`0.61` + z\sqrt{\frac{`0.61` \times (1-`0.61`)}{350}} = 0.6528$ | M1 | oe |
| $z = 0.0428 \times \sqrt{\frac{700}{`0.61` \times (1-`0.61`)}}$ oe | M1 | correct rearrangement of correct equation, ft '0.61' |
| $= 2.321$ | A1 | |
| 98% confidence | A1ft [4] | ft their $z$ (dep on both Ms) |
---3 Based on a random sample of 700 people living in a certain area, a confidence interval for the proportion, $p$, of all people living in that area who had travelled abroad was found to be $0.5672 < p < 0.6528$.\\
(i) Find the proportion of people in the sample who had travelled abroad.\\
(ii) Find the confidence level of this confidence interval. Give your answer correct to the nearest integer.
\hfill \mbox{\textit{CAIE S2 2016 Q3 [5]}}