Mathematics 9709 · AS & A Level · Sampling and estimation
Sampling and estimation — practice question
Sunita owns a six-sided die with faces numbered 1, 2, 3, 4, 5, 6. The probability that one throw gives a six is $p$. She throws the die 500 times and records 70 sixes.
(a)[4]
Calculate an approximate 99% confidence interval for $p$.
(b)[1]
Sunita thinks the die is fair. Use your result from part (a) to comment on that belief.
(c)[5]
Sunita uses the outcome of her 500 throws to form an $\alpha\%$ confidence interval for $p$. The interval’s width is $0.04$. Determine $\alpha$.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Sample proportion correctly found as $p=\frac{70}{500}=0.14$” …