Mathematics 9709 · AS & A Level · Sampling and estimation
Sampling and estimation — practice question
Let the times, measured in minutes, for students finishing a test have mean $\mu$ and standard deviation $\sigma$. A random sample of 100 students is recorded, and the data are then used to construct a 95% confidence interval for $\mu$.
(a)[3]
Using the 95% confidence interval endpoints 31.02 and 33.98, each correct to 4 significant figures, determine $\sigma$.
(b)[1]
Explain why it is valid in this situation to use the Central Limit theorem when finding the confidence interval.
(c)[4]
A researcher finds $r$ separate 95% confidence intervals for $\mu$. Determine the greatest value of $r$ for which the probability that every one of the $r$ confidence intervals contains the true value of $\mu$ exceeds 0.5.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Use the sample mean $32.5$ or the width $2.96$.” …