| Exam Board | CAIE |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2020 |
| Session | Specimen |
| Marks | 4 |
| Paper | 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 σ, requiring only substitution into z × σ/√n. Part (b) tests conceptual understanding of confidence intervals but is a standard textbook question about the symmetric property of CIs. Minimal problem-solving required; primarily recall and routine calculation. |
| Spec | 5.05d Confidence intervals: using normal distribution |
Leaves from a certain type of tree have lengths that are distributed with standard deviation 3 cm. A random sample of 6 of these leaves is taken and the mean length of this sample is found to be 8 cm.
\begin{enumerate}[label=(\alph*)]
\item Calculate a 95\% confidence interval for the population mean length. [3]
\item Write down the probability that the whole 95\% confidence interval will lie below the population mean. [1]
\end{enumerate}
\hfill \mbox{\textit{CAIE S2 2020 Q1 [4]}}