| Exam Board | CAIE |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2016 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Hypothesis test of a Poisson distribution |
| Type | Find critical region |
| Difficulty | Standard +0.3 This is a straightforward hypothesis testing question requiring standard Poisson distribution calculations. Students need to find a critical region (routine procedure), compare the test statistic, and recall definitions of Type I and Type II errors. While it involves multiple parts, each step follows textbook procedures with no novel insight required, making it slightly easier than average. |
| Spec | 2.05a Hypothesis testing language: null, alternative, p-value, significance5.05b Unbiased estimates: of population mean and variance |
The number of sightings of a golden eagle at a certain location has a Poisson distribution with mean 2.5 per week. Drilling for oil is started nearby. A naturalist wishes to test at the 5\% significance level whether there are fewer sightings since the drilling began. He notes that during the following 3 weeks there are 2 sightings.
\begin{enumerate}[label=(\roman*)]
\item Find the critical region for the test and carry out the test. [5]
\item State the probability of a Type I error. [1]
\item State why the naturalist could not have made a Type II error. [1]
\end{enumerate}
\hfill \mbox{\textit{CAIE S2 2016 Q4 [7]}}