Mathematics 9709 · AS & A Level · Hypothesis testing
Hypothesis testing — practice question
The number of cars that reach a particular road junction on a weekday morning follows a Poisson distribution with mean $4.6$ per minute. Traffic lights are fitted at the junction, and a council officer wants to test at the $2\%$ significance level whether fewer cars are now arriving. He records the number of cars that arrive in one randomly selected $2$-minute interval.
(a)[1]
State suitable null and alternative hypotheses for this test.
(b)[4]
Find the critical region for this test.
(c)[2]
The officer records that, in one randomly chosen $2$-minute interval on a weekday morning, exactly $5$ cars arrive at the junction. Carry out the test.
(d)[1]
State, with a reason, whether a Type I error could have been made when carrying out the test in part (c).
(e)[3]
The number of cars arriving at another junction on a weekday morning also has a Poisson distribution with mean $4.6$ per minute. Use a suitable approximating distribution to find the probability that more than $300$ cars will arrive at this junction in an hour.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Correct hypotheses are $H_0: \mu = 4.6$ (or $9.2$) and $H_1: \mu < 4.6$ (or $9.2$)” …