Mathematics 9709 · AS & A Level · Hypothesis testing
Hypothesis testing — practice question
The fraction of people who have a certain medical condition is $1$ in $100\,000$. A random sample of $2500$ people is taken. Let $X$ represent the number of people in the sample who have the condition.
(a(i))[2]
State, with a justification, an appropriate approximating distribution for $X$, and include the values of any parameters.
(a(ii))[2]
Use the approximating distribution to find $P(X > 0)$.
(b)[5]
Apply a binomial distribution to test the researcher’s suspicion at the $2\%$ significance level.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “State that $X$ follows $\text{Po}(0.025)$.” …