| Exam Board | Edexcel |
|---|---|
| Module | S2 (Statistics 2) |
| Marks | 15 |
| Paper | Download PDF ↗ |
| Topic | Hypothesis test of a Poisson distribution |
| Type | One-tailed test (increase or decrease) |
| Difficulty | Standard +0.3 This is a straightforward S2 hypothesis testing question requiring standard Poisson distribution application. Parts (a) and (b) involve routine model identification and probability calculation with parameter scaling. Part (c) is a textbook one-tailed hypothesis test with clear structure. Part (d) tests conceptual understanding of Poisson assumptions. While it requires multiple techniques, each step follows standard procedures with no novel insight needed, making it slightly easier than average A-level difficulty. |
| Spec | 2.04e Normal distribution: as model N(mu, sigma^2)2.05b Hypothesis test for binomial proportion2.05c Significance levels: one-tail and two-tail5.02i Poisson distribution: random events model5.02j Poisson formula: P(X=x) = e^(-lambda)*lambda^x/x!5.02l Poisson conditions: for modelling |
A doctor expects to see, on average, 1 patient per week with a particular disease.
\begin{enumerate}[label=(\alph*)]
\item Suggest a suitable model for the distribution of the number of times per week that the doctor sees a patient with the disease. Give a reason for your answer. [3]
\item Using your model, find the probability that the doctor sees more than 3 patients with the disease in a 4 week period. [4]
\end{enumerate}
The doctor decides to send information to his patients to try to reduce the number of patients he sees with the disease. In the first 6 weeks after the information is sent out, the doctor sees 2 patients with the disease.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Test, at the 5\% level of significance, whether or not there is reason to believe that sending the information has reduced the number of times the doctor sees patients with the disease. State your hypotheses clearly. [6]
\end{enumerate}
Medical research into the nature of the disease discovers that it can be passed from one patient to another.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{3}
\item Explain whether or not this research supports your choice of model. Give a reason for your answer. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S2 Q6 [15]}}