Mathematics 9709 · AS & A Level · Sampling and estimation
Sampling and estimation — practice question
For any one spin, the chance that a particular spinner lands on red is $p$. The spinner is spun $140$ times, and red appears $35$ times.
(a)[3]
Calculate an approximate $96\%$ confidence interval for $p$.
(b)[3]
Jack carries out three more experiments and obtains a $90\%$ confidence interval, a $95\%$ confidence interval and a $99\%$ confidence interval for $p$. Find the probability that exactly two of these confidence intervals contain the true value of $p$.
Worked solution & mark scheme
This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Applies confidence interval form $0.25\pm z\sqrt{\frac{0.25\times0.75}{140}}$” …