Standard +0.3 This is a straightforward hypothesis test for a Poisson mean with clearly defined hypotheses (H₀: λ=2.5 vs H₁: λ>2.5), requiring students to scale the parameter for 4 weeks (λ=10), calculate P(X≥14), and compare to 5%. While it involves multiple steps, it's a standard textbook application of Poisson hypothesis testing with no conceptual surprises, making it slightly easier than average.
The number of houses sold per week by a firm of estate agents follows a Poisson distribution with mean 2.5. The firm appoints a new salesman and wants to find out whether or not house sales increase as a result. After the appointment of the salesman, the number of house sales in a randomly chosen 4-week period is 14.
Stating your hypotheses clearly test, at the 5\% level of significance, whether or not the new salesman has increased house sales. [7]
The number of houses sold per week by a firm of estate agents follows a Poisson distribution with mean 2.5. The firm appoints a new salesman and wants to find out whether or not house sales increase as a result. After the appointment of the salesman, the number of house sales in a randomly chosen 4-week period is 14.
Stating your hypotheses clearly test, at the 5\% level of significance, whether or not the new salesman has increased house sales. [7]
\hfill \mbox{\textit{Edexcel S2 Q2 [7]}}