Standard +0.3 This is a straightforward hypothesis test for a Poisson mean with clear setup. Students must recognize to scale the parameter (0.31 × 5 = 1.55), set up H₀: λ = 1.55 vs H₁: λ > 1.55, and calculate P(X ≥ 5) using tables or cumulative probabilities. While it requires careful handling of the one-tailed test and comparison with 2.5%, it's a standard application of taught procedures with no conceptual surprises—slightly easier than average due to explicit guidance that Poisson is appropriate and clear statement of what changed.
In the past the number of enquiries per minute at a customer service desk has been modelled by a random variable with distribution Po(0.31). Following a change in the position of the desk, it is expected that the mean number of enquiries per minute will increase. In order to test whether this is the case, the total number of enquiries during a randomly chosen 5-minute period is noted. You should assume that a Poisson model is still appropriate.
Given that the total number of enquiries is 5, carry out the test at the 2.5% significance level. [5]
In the past the number of enquiries per minute at a customer service desk has been modelled by a random variable with distribution Po(0.31). Following a change in the position of the desk, it is expected that the mean number of enquiries per minute will increase. In order to test whether this is the case, the total number of enquiries during a randomly chosen 5-minute period is noted. You should assume that a Poisson model is still appropriate.
Given that the total number of enquiries is 5, carry out the test at the 2.5% significance level. [5]
\hfill \mbox{\textit{CAIE S2 2023 Q5 [5]}}