(a)[3]
Calculate an estimate of the standard deviation of the population.
(b)[1]
Explain whether it was necessary to use the Central Limit Theorem in your response to part (a).
Mathematics 9709 · AS & A Level · Sampling and estimation
Sampling and estimation — practice question
The widths, $w$ cm, of a random sample of $150$ leaves of a particular type were measured. The sample mean of $w$ was $3.12\,\text{cm}$. From this sample, an approximate $95\%$ confidence interval for the population mean width, in centimetres, was obtained as $[3.01,\,3.23]$.
Worked solution & mark scheme
This 4-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Set up the confidence-interval equation as $3.12+z\frac{\sigma}{\sqrt{150}}=3.23$.” …
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