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 $4.96$

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