| Exam Board | OCR |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2010 |
| Session | January |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Hypothesis test of a Poisson distribution |
| Type | Test with normal approximation |
| Difficulty | Standard +0.3 This is a straightforward one-tailed hypothesis test for a Poisson mean with clear setup (H₀: λ=11, H₁: λ>11) and standard procedure. Part (i) requires calculating P(X≥19) using tables and comparing to 5%, which is routine S2 material. Part (ii) is a simple conceptual comment about correlation vs causation. Slightly easier than average due to explicit guidance and standard test structure. |
| Spec | 2.05b Hypothesis test for binomial proportion |
The number of customers arriving at a store between 8.50 am and 9 am on Saturday mornings is a random variable which can be modelled by the distribution Po(11.0). Following a series of price cuts, on one particular Saturday morning 19 customers arrive between 8.50 am and 9 am. The store's management claims, first, that the mean number of customers has increased, and second, that this is due to the price cuts.
\begin{enumerate}[label=(\roman*)]
\item Test the first part of the claim, at the 5% significance level. [7]
\item Comment on the second part of the claim. [1]
\end{enumerate}
\hfill \mbox{\textit{OCR S2 2010 Q5 [8]}}