| Exam Board | CAIE |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2022 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Confidence intervals |
| Type | Calculate CI from summary stats |
| Difficulty | Moderate -0.3 Part (a) is a standard confidence interval calculation with known sample statistics requiring lookup of z-value and formula application. Part (b) tests understanding of random sampling assumptions but requires only brief conceptual commentary. Straightforward application of routine techniques with minimal problem-solving. |
| Spec | 2.01c Sampling techniques: simple random, opportunity, etc5.05b Unbiased estimates: of population mean and variance5.05d Confidence intervals: using normal distribution |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(72.3 \pm z\sqrt{\dfrac{64.3}{50}}\) | M1 | Expression of correct form (allow only one side for M1). Must be a \(z\) value |
| \(z = 1.751\) | B1 | Accept 1.75 if nothing better seen |
| CI is 70.3 to 74.3 metres (3 s.f.) | A1 | Allow without units. Must be an interval |
| 3 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Not random sample | B1 | Need 'random' or 'not representative/biased because…' OE |
| 1 |
**Question 1:**
**Part (a):**
| Answer | Mark | Guidance |
|--------|------|----------|
| $72.3 \pm z\sqrt{\dfrac{64.3}{50}}$ | M1 | Expression of correct form (allow only one side for M1). Must be a $z$ value |
| $z = 1.751$ | B1 | Accept 1.75 if nothing better seen |
| CI is 70.3 to 74.3 metres (3 s.f.) | A1 | Allow without units. Must be an interval |
| | **3** | |
**Part (b):**
| Answer | Mark | Guidance |
|--------|------|----------|
| Not random sample | B1 | Need 'random' or 'not representative/biased because…' OE |
| | **1** | |1
\begin{enumerate}[label=(\alph*)]
\item A javelin thrower noted the lengths of a random sample of 50 of her throws. The sample mean was 72.3 m and an unbiased estimate of the population variance was $64.3 \mathrm {~m} ^ { 2 }$.
Find a $92 \%$ confidence interval for the population mean length of throws by this athlete.
\item A discus thrower wishes to calculate a $92 \%$ confidence interval for the population mean length of his throws. He bases his calculation on his first 50 throws in a week.
Comment on this method.
\end{enumerate}
\hfill \mbox{\textit{CAIE S2 2022 Q1 [4]}}