Mathematics 9709 · AS & A Level · Sampling and estimation

Sampling and estimation — practice question

From a random sample of 100 students at Luciana’s college, $x$ reported that they liked exams. She then used these data to calculate an approximate 90\% confidence interval for the proportion, $p$, of all students at her college apresentado who liked exams. The interval width was $0.15792$.
(a)[4]

Find the two values that $x$ can take.

(b)[1]

Find the probability that neither confidence interval includes the true value of $p$.

Worked solution & mark scheme

This 5-mark question has a full step-by-step worked solution and mark scheme. One marking point: The correct critical value is $z = 1.645$.

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