Mathematics 9709 · AS & A Level · Hypothesis testing
Hypothesis testing — practice question
For a given population, the chance that one person has this specific medical condition is $1$ in $100\,000$. A random selection of $2500$ people is then taken. Let $X$ denote the number of people in the sample who have the condition.
(a(i))[2]
State, with justification, a suitable approximating distribution for $X$, giving the values of any parameters.
(a(ii))[2]
Apply the approximating distribution to find $P(X > 0)$.
(b)[5]
The percentage of people with a different medical condition is believed to be $30\%$. A researcher thinks that the true percentage is below $30\%$. In a medical trial, a random sample of $28$ people was chosen and $4$ people were found to have this condition. Use 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: “Applies the Poisson distribution $\text{Po}(0.025)$” …