Mathematics 9709 · AS & A Level · Sampling and estimation
Sampling and estimation — practice question
For a random sample of 200 discs produced by one machine, the diameters, $x$ millimetres, were measured and written down. The summary data are as follows: $n = 200$, $\sum x = 2520$, $\sum x^2 = 31852$.
(a)[6]
Calculate a 95% confidence interval for the mean diameter of the population.
(b)[1]
Jean selected 40 random samples and used each one to work out a 95% confidence interval for the population mean diameter. For how many of these 40 confidence intervals would you expect the true value of the population mean diameter to lie inside?
Worked solution & mark scheme
This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Finds the mean estimate $\mu = \frac{2520}{200} = 12.6$” …