| Exam Board | CAIE |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Year | 2014 |
| Session | June |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Confidence intervals |
| Type | CI from raw data list |
| Difficulty | Standard +0.3 This is a straightforward application of t-test and confidence interval formulas for small samples from a normal distribution. Students must calculate sample mean and standard deviation, then apply standard procedures with t-tables. While it requires careful arithmetic and knowledge of the t-distribution, it involves no conceptual challenges or novel problem-solving—just routine statistical inference techniques that are directly taught and practiced. |
| Spec | 5.05c Hypothesis test: normal distribution for population mean5.05d Confidence intervals: using normal distribution |
10 The lengths of a random sample of eight fish of a certain species are measured, in cm, as follows.
$$\begin{array} { l l l l l l l l }
17.3 & 15.8 & 18.2 & 15.6 & 16.0 & 18.8 & 15.3 & 15.0
\end{array}$$
Assuming that lengths are normally distributed,\\
(i) test, at the $10 \%$ significance level, whether the population mean length of fish of this species is greater than 15.8 cm ,\\
(ii) calculate a $95 \%$ confidence interval for the population mean length of fish of this species.
\hfill \mbox{\textit{CAIE FP2 2014 Q10}}