Mathematics 9709 · AS & A Level · Sampling and estimation
Sampling and estimation — practice question
A random sample of $75$ students was used to record the completion times, $T$ minutes, for a test. The summary totals were $\Sigma t = 230$ and $\Sigma t^2 = 930$.
(a)[3]
Calculate unbiased estimates for the population mean and the variance of $T$.
(b)[3]
The times taken by another random sample of $75$ students were recorded, and the sample mean, $\bar{T}$, was obtained. Determine the value of $a$ for which $P(\bar{T} > a) = 0.234$. You should assume that the values estimated in part (a) are the true 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 $\bar t=\dfrac{230}{75}=3.0666\ldots$ or $3.07$” …