| Exam Board | Edexcel |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2003 |
| Session | January |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Hypothesis test of a Poisson distribution |
| Type | Two-tailed test setup or execution |
| Difficulty | Standard +0.8 This S2 question requires understanding of two-tailed hypothesis tests with discrete distributions, finding critical regions by calculating cumulative Poisson probabilities to get as close as possible to 2.5% in each tail, recognizing that the actual significance level differs from the nominal level due to discreteness, and applying the decision rule. While methodical, it demands more sophistication than routine one-tailed tests and careful handling of discrete probability constraints. |
| Spec | 5.02i Poisson distribution: random events model5.02j Poisson formula: P(X=x) = e^(-lambda)*lambda^x/x!5.02k Calculate Poisson probabilities5.05b Unbiased estimates: of population mean and variance |
2. A single observation $x$ is to be taken from a Poisson distribution with parameter $\lambda$. This observation is to be used to test $\mathrm { H } _ { 0 } : \lambda = 7$ against $\mathrm { H } _ { 1 } : \lambda \neq 7$.
\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 $2.5 \%$.
\item Write down the significance level of this test.
The actual value of $x$ obtained was 5 .
\item State a conclusion that can be drawn based on this value.
\end{enumerate}
\hfill \mbox{\textit{Edexcel S2 2003 Q2 [8]}}