(a)[2]
Find the probability that a Type I error occurs.
(b)[3]
Find the probability of a Type II error if the actual mean number of accidents per 3-month period is $0.9$.
Mathematics 9709 · AS & A Level · Hypothesis testing
Hypothesis testing — practice question
For a certain road, the number of accidents in each 3-month period follows the distribution $\text{Po}(\lambda)$. Historically, $\lambda$ has had the value $5.7$. After some changes to the road, the council carries out a hypothesis test to decide whether $\lambda$ has fallen. If a randomly chosen 3-month period contains fewer than $3$ accidents, the council will decide that $\lambda$ has decreased.
Worked solution & mark scheme
This 5-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Correct Poisson formula, e.g. $e^{-5.7}\left(1+5.7+\frac{5.7^2}{2!}\right)$” …
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