OCR S2 2010 January — Question 5 8 marks

Exam BoardOCR
ModuleS2 (Statistics 2)
Year2010
SessionJanuary
Marks8
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Mark schemeDownload PDF ↗
TopicHypothesis test of a Poisson distribution
TypeTest with normal approximation
DifficultyStandard +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.
Spec2.05b 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.
  1. Test the first part of the claim, at the 5% significance level. [7]
  2. Comment on the second part of the claim. [1]

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]}}