| Exam Board | Edexcel |
|---|---|
| Module | S4 (Statistics 4) |
| Year | 2004 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Hypothesis test of a Poisson distribution |
| Type | Two-tailed test setup or execution |
| Difficulty | Challenging +1.2 This is a standard S4 hypothesis testing question requiring Poisson table lookups and understanding of Type II errors. While it involves multiple parts and requires careful probability calculations from tables, the concepts are routine for Further Maths Statistics 4 students with no novel problem-solving required—just methodical application of learned procedures. |
| Spec | 2.05a Hypothesis testing language: null, alternative, p-value, significance5.02i Poisson distribution: random events model5.02j Poisson formula: P(X=x) = e^(-lambda)*lambda^x/x! |
3. It is suggested that a Poisson distribution with parameter $\lambda$ can model the number of currants in a currant bun. A random bun is selected in order to test the hypotheses $\mathrm { H } _ { 0 } : \lambda = 8$ against $\mathrm { H } _ { 1 } : \lambda \neq 8$, using a $10 \%$ level of significance.
\begin{enumerate}[label=(\alph*)]
\item Find the critical region for this test, such that the probability in each tail is as close as possible to $5 \%$.
\item Given that $\lambda = 10$, find
\begin{enumerate}[label=(\roman*)]
\item the probability of a type II error,
\item the power of the test.\\
(4)
\end{enumerate}\end{enumerate}
\hfill \mbox{\textit{Edexcel S4 2004 Q3 [9]}}