Mathematics 9709 · AS & A Level · Hypothesis testing
Hypothesis testing — practice question
The annual count of accidents on a particular road follows the distribution $\text{Po}(\lambda)$. In the past, the value of $\lambda$ was $3.3$. A new speed limit has now been introduced, and the council wants to check whether $\lambda$ has fallen. It records the total number, $X$, of accidents over two randomly selected years after the speed limit was introduced and performs a test at the $5\%$ significance level.
(a)[4]
Calculate the probability associated with a Type I error.
(b)[3]
When $X = 2$, carry out the test.
(c)[3]
At the $5\%$ significance level, the council carries out another similar test with the same hypotheses and two different randomly chosen years. If the true value of $\lambda$ is $0.6$, calculate the probability of a Type II error.
(d)[4]
Using $\lambda = 0.6$ and a suitable approximating distribution, find the probability that there will be more than $10$ accidents in $30$ years.
Worked solution & mark scheme
This 14-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Correct mean is $\lambda=6.6$” …