Mathematics 9709 · AS & A Level · Sampling and estimation
Sampling and estimation — practice question
For a random sample of $90$ sacks of flour, the masses, $m$ kilograms, are summarised by $n = 90$, $\sum m = 4509$, $\sum m^2 = 225\,950$.
(a)[3]
Find unbiased estimates for the population mean and for the variance.
(b)[3]
Calculate a $98\%$ confidence interval for the population mean.
(c)[1]
Explain why the Central Limit Theorem had to be used when answering part (b).
(d)[2]
Find the probability that the confidence interval obtained in part (b) lies entirely above the true value of the population mean.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Calculate $\bar{x} = \dfrac{4509}{90} = 50.1$ for the sample mean.” …