Hypothesis testing conceptsEdexcel International A Level Further Maths: Mind map

Exam questions on Hypothesis testing concepts

1. A coin is suspected of being biased towards heads. It is tossed $20$ times and $X$ is the number of heads. Let $p$ be the probability of heads on one toss.
   At the $5\%$ significance level, the critical region is $X\ge15$. Explain what is meant by the critical region, and state the conclusion if $16$ heads are observed.2 marks
2. Before a timetable change, the number of late arrivals at an airport gate each day was modelled by a Poisson distribution with mean $4$. After the change, the manager wants to test whether the mean number $\lambda$ of late arrivals per day is different, using the number $X$ of late arrivals on a randomly chosen day.
   The manager says that the test is being used to refine the model. Explain how the test helps to refine the model.2 marks
3. A teacher gives a pupil $20$ true/false questions to test whether the pupil is just guessing. Let $X$ be the number of questions answered correctly and $p$ the probability that the pupil answers a question correctly. The teacher tests $\mathrm{H}_0:p=0.5$ against $\mathrm{H}_1:p\ne0.5$ at the $5\%$ significance level, with $2.5\%$ in each tail. A calculator may be used.
   Find the critical region for the test.3 marks