Mathematics 9709 · AS & A Level · Sampling and estimation
Sampling and estimation — practice question
A coffee machine fills cups with coffee. The quantity of coffee in a cup, $V$ cm$^3$, was recorded for a random sample of $150$ cups. The findings were summarised as follows: $\sum v = 46\,350$, $\sum v^2 = 14\,410\,800$.
(a(i))[3]
Calculate unbiased estimates for the population mean, $\mu$, and the population variance, $\sigma^2$.
(a(ii))[3]
Calculate a $95\%$ confidence interval for $\mu$.
(b)[2]
Without doing any calculation, state whether this confidence interval would be wider or narrower than the interval found in part (a)(ii). Give a reason for your response.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Determine estimated mean $\hat{\mu}=\frac{46350}{150}=309$” …