| Exam Board | Edexcel |
|---|---|
| Module | S4 (Statistics 4) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Topic | T-tests (unknown variance) |
| Type | Validity and assumptions questions |
| Difficulty | Challenging +1.2 This is a standard S4 hypothesis testing question requiring critical region calculation for a Poisson distribution and understanding of Type II error/power. While it involves multiple steps and requires careful use of tables, the concepts are core syllabus material with no novel insight needed. The two-tailed test and power calculation add moderate complexity beyond routine exercises, placing it slightly above average difficulty. |
| Spec | 2.05a Hypothesis testing language: null, alternative, p-value, significance2.05b Hypothesis test for binomial proportion5.02i Poisson distribution: random events model5.02k Calculate Poisson probabilities |
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 H₀: $\lambda = 8$ against H₁: $\lambda \neq 8$, 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\%. [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 Q3 [9]}}