| Exam Board | CAIE |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2024 |
| Session | November |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Confidence intervals |
| Type | Calculate CI from summary stats |
| Difficulty | Moderate -0.8 Part (a) is a direct application of the standard confidence interval formula with known population standard deviation—purely procedural with no conceptual challenge. Part (b) tests understanding of what a confidence interval means, which is a common misconception question but requires only brief recall of the correct interpretation rather than any problem-solving. |
| Spec | 5.05d Confidence intervals: using normal distribution |
| Answer | Marks | Guidance |
|---|---|---|
| 1(a) | z = 2.054 or 2.055 | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| 150 | M1 | Must be a z value. |
| 1.36 to 1.48 [m] (3 sf) | A1 | Correct working only. Must be an interval. |
| Answer | Marks | Guidance |
|---|---|---|
| 1(b) | No. CI is about mean, not individual values. | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Question | Answer | Marks |
Question 1:
--- 1(a) ---
1(a) | z = 2.054 or 2.055 | B1 | Accept 3 sf if nothing better seen (2.05 or 2.06).
0.35
1.42 ± z
150 | M1 | Must be a z value.
1.36 to 1.48 [m] (3 sf) | A1 | Correct working only. Must be an interval.
3
--- 1(b) ---
1(b) | No. CI is about mean, not individual values. | B1 | Or similar. Need both.
1
Question | Answer | Marks | GuidanceThe heights of a certain species of deer are known to have standard deviation $0.35$ m. A zoologist takes a random sample of $150$ of these deer and finds that the mean height of the deer in the sample is $1.42$ m.
\begin{enumerate}[label=(\alph*)]
\item Calculate a $96\%$ confidence interval for the population mean height. [3]
\item Bubay says that $96\%$ of deer of this species are likely to have heights that are within this confidence interval.
Explain briefly whether Bubay is correct. [1]
\end{enumerate}
\hfill \mbox{\textit{CAIE S2 2024 Q1 [4]}}