Mathematics 9709 · AS & A Level · Sampling and estimation
Sampling and estimation — practice question
A random sample of 7 leaves taken from one particular tree variety has lengths, $X$ centimetres, listed below:
$5.2, 4.8, 5.5, 6.1, 4.8, 3.9, 4.4$.
(a)[3]
Calculate unbiased estimates for the population mean and variance of $X$.
(b)[3]
It is now given that the true value of the population variance of $X$ is $0.55$, and that $X$ has a normal distribution. Find a $95\%$ confidence interval for the population mean of $X$.
Worked solution & mark scheme
This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Mean formula used $\bar{x} = \frac{\sum x}{n} = \frac{34.7}{7} = 4.9571$ or $4.96$” …