| Exam Board | Edexcel |
|---|---|
| Module | S4 (Statistics 4) |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Topic | Hypothesis test of a Poisson distribution |
| Type | Find Type I error probability |
| Difficulty | Standard +0.3 This is a straightforward hypothesis testing question on Poisson distributions with standard Type I/II error calculations. Part (a) requires definition recall, part (b) is a routine one-tailed Poisson test, and parts (c)-(d) involve direct probability calculations from tables. While it requires understanding of error types and careful probability work, all components are standard S4 material with no novel problem-solving required. |
| Spec | 2.05a Hypothesis testing language: null, alternative, p-value, significance5.02i Poisson distribution: random events model5.02k Calculate Poisson probabilities |
\begin{enumerate}[label=(\alph*)]
\item Define
\begin{enumerate}[label=(\roman*)]
\item a Type I error,
\item a Type II error. [2]
\end{enumerate}
\end{enumerate}
A small aviary, that leaves the eggs with the parent birds, rears chicks at an average rate of 5 per year. In order to increase the number of chicks reared per year it is decided to remove the eggs from the aviary as soon as they are laid and put them in an incubator. At the end of the first year of using an incubator 7 chicks had been successfully reared.
\begin{enumerate}[label=(\alph*)]
\item[(b)] Assuming that the number of chicks reared per year follows a Poisson distribution test, at the 5\% significance level, whether or not there is evidence of an increase in the number of chicks reared per year. State your hypotheses clearly. [4]
\item Calculate the probability of the Type I error for this test. [3]
\item Given that the true average number of chicks reared per year when the eggs are hatched in an incubator is 8, calculate the probability of a Type II error. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S4 Q5 [11]}}