| Exam Board | Edexcel |
|---|---|
| Module | S2 (Statistics 2) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | Hypothesis test of a Poisson distribution |
| Type | Two-tailed test setup or execution |
| Difficulty | Standard +0.3 This is a standard S2 hypothesis testing question requiring calculation of critical regions for a Poisson distribution using tables. While it involves a two-tailed test and requires careful probability calculations, the procedure is routine and well-practiced. The question is slightly easier than average because it's a single observation (simpler than sample means), follows a standard template, and the calculations are straightforward with provided tables. |
| Spec | 2.05b Hypothesis test for binomial proportion2.05c Significance levels: one-tail and two-tail |
A single observation x is to be taken from a Poisson distribution with parameter $\lambda$. This observation is to be used to test H₀: $\lambda$ = 7 against H₁: $\lambda$ ≠ 7.
\begin{enumerate}[label=(\alph*)]
\item Using a 5\% significance level, find the critical region for this test assuming that the probability of rejection in either tail is as close as possible to 2.5\%. [5]
\item Write down the significance level of this test. [1]
\end{enumerate}
The actual value of x obtained was 5.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item State a conclusion that can be drawn based on this value. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S2 Q2 [8]}}