| Exam Board | CAIE |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2011 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Z-tests (known variance) |
| Type | Confidence interval with known population standard deviation |
| Difficulty | Moderate -0.3 This is a straightforward application of z-test confidence intervals with known variance. Students must calculate the sample mean, apply the standard CI formula with z-critical value, and make basic interpretations. While it requires multiple steps and understanding of when CLT applies, it's a textbook exercise with no novel problem-solving—slightly easier than average due to clear structure and routine calculations. |
| Spec | 5.05a Sample mean distribution: central limit theorem5.05d Confidence intervals: using normal distribution |
A doctor wishes to investigate the mean fat content in low-fat burgers. He takes a random sample of 15 burgers and sends them to a laboratory where the mass, in grams, of fat in each burger is determined. The results are as follows.
$9 \quad 7 \quad 8 \quad 9 \quad 6 \quad 11 \quad 7 \quad 9 \quad 8 \quad 9 \quad 8 \quad 10 \quad 7 \quad 9 \quad 9$
Assume that the mass, in grams, of fat in low-fat burgers is normally distributed with mean $\mu$ and that the population standard deviation is 1.3.
\begin{enumerate}[label=(\roman*)]
\item Calculate a 99\% confidence interval for $\mu$. [4]
\item Explain whether it was necessary to use the Central Limit theorem in the calculation in part (i). [2]
\item The manufacturer claims that the mean mass of fat in burgers of this type is 8 g. Use your answer to part (i) to comment on this claim. [2]
\end{enumerate}
\hfill \mbox{\textit{CAIE S2 2011 Q4 [8]}}