Mathematics 9709 · AS & A Level · Sampling and estimation
Sampling and estimation — practice question
The completion times, $T$ minutes, for a random sample of 75 students doing a test were recorded. The data were summarised by $\Sigma t = 230$ and $\Sigma t^2 = 930$.
(a)[3]
Calculate unbiased estimates for the population mean and variance of $T$.
(b)[3]
The times for another random sample of 75 students were recorded, and the sample mean, $\overline{T}$, was obtained. Find the value of $a$ such that $P(\overline{T} > a) = 0.234$. Assume that the estimates from part (a) are the actual values of the population mean and variance of $T$.
Worked solution & mark scheme
This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Correct mean value $\bar t=\frac{230}{75}=3.07$ (3 s.f.)” …