Mathematics 9709 · AS & A Level · Hypothesis testing
Hypothesis testing — practice question
A new light was fitted along a footpath. A town councillor chose to use a hypothesis test to check whether the number of people using the path in the evening had risen.
Before the light was fitted, the mean number of people using the path in any 20-minute period in the evening was $1.01$.
Once the light had been fitted, the total number, $n$, of people using the path in 3 randomly selected 20-minute periods in the evening was recorded.
(a)[6]
With $n=6$, use a Poisson distribution to perform the test at the $5\%$ significance level.
(b)[2]
A similar test was later carried out at the $5\%$ significance level, using another 3 randomly selected 20-minute periods in the evening. Find the probability of a Type I error.
(c)[1]
State what a Type I error means in this context.
(d)[2]
State, in context, what additional information would be required to find the probability of a Type II error. Do not do any further calculation.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Valid hypotheses for the Poisson mean, e.g. $H_0: \lambda = 3.03$, $H_1: \lambda > 3.03$” …