| Exam Board | Edexcel |
|---|---|
| Module | FS1 (Further Statistics 1) |
| Session | Specimen |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Poisson distribution |
| Type | Poisson hypothesis test |
| Difficulty | Standard +0.3 This is a straightforward one-tailed Poisson hypothesis test with clear setup. Students must identify λ=2.5 for 0.5L, state H₀: λ=2.5 vs H₁: λ>2.5, calculate P(X≥7), and compare to 5%. The context is given explicitly, requiring only standard application of Poisson tables/calculation with no conceptual subtleties or multi-step reasoning beyond the standard hypothesis test framework. |
| Spec | 5.02i Poisson distribution: random events model5.02j Poisson formula: P(X=x) = e^(-lambda)*lambda^x/x!5.02k Calculate Poisson probabilities5.05c Hypothesis test: normal distribution for population mean |
\begin{enumerate}
\item Bacteria are randomly distributed in a river at a rate of 5 per litre of water. A new factory opens and a scientist claims it is polluting the river with bacteria. He takes a sample of 0.5 litres of water from the river near the factory and finds that it contains 7 bacteria. Stating your hypotheses clearly test, at the $5 \%$ level of significance, whether there is evidence that the level of pollution has increased.
\end{enumerate}
\section*{Q uestion 1 continued}
\hfill \mbox{\textit{Edexcel FS1 Q1 [5]}}