Mathematics 9709 · AS & A Level · Hypothesis testing
Hypothesis testing — practice question
The weekly count of accidents at one factory follows a Poisson distribution. In previous years, the mean has been $1.9$ accidents per week. Last year, the manager issued every employee a new safety booklet. He wishes to test, at the $5\%$ significance level, whether the average number of accidents has gone down. He records the accident count for $4$ weeks selected at random this year.
(a)[1]
Give appropriate null and alternative hypotheses for this test.
(b)[6]
Determine the critical region for the test and give the probability of a Type I error.
(c)[1]
Give the meaning of a Type I error in this context.
(d)[2]
Over the $4$ randomly selected weeks, there is a total of $3$ accidents. State the conclusion the manager should draw, and justify your answer.
(e)[4]
If the mean stays at $1.9$ accidents per week, use an appropriate approximation to find the probability that more than $100$ accidents occur in a $52$-week interval.
Worked solution & mark scheme
This 14-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Write $H_0:\lambda=7.6$ and $H_1:\lambda<7.6$ (or the equivalent population mean form).” …