Mathematics 9709 · AS & A Level · Sampling and estimation
Sampling and estimation — practice question
Heights, $h$ centimetres, were recorded for a random sample of $100$ fully grown animals of a particular species. The summary is given below.
$n = 100 \qquad \Sigma h = 7570 \qquad \Sigma h^2 = 588\,050$
(a)[3]
Find unbiased estimates of the population mean and variance.
(b)[3]
Calculate a $99\%$ confidence interval for the mean height of animals of this species.
(c)[2]
Four random samples were taken and a $99\%$ confidence interval for the population mean, $\mu$, was found from each sample. Find the probability that all four of these confidence intervals contain the true value of $\mu$.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Mean estimate $\hat\mu=\dfrac{7570}{100}=75.7$” …