(a)[3]
Find the value of $\alpha$.
(b)[1]
Find the probability that the 90% confidence interval includes the population mean, given that the $\alpha\%$ confidence interval includes the population mean.
Mathematics 9709 · AS & A Level · Sampling and estimation
Sampling and estimation — practice question
The masses of a certain animal species are assumed to follow a normal distribution with standard deviation $\sigma$ kg. A researcher measures the masses of a random sample of $n$ animals from this species and uses them to form two confidence intervals, one at $\alpha\%$ and the other at 90%, for the population mean. The width of the $\alpha\%$ confidence interval is 1.414 times the width of the 90% confidence interval.
Worked solution & mark scheme
This 4-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Using the interval widths gives $2\times1.645\times\frac{\sigma}{\sqrt{n}}=1.414\times z\times\frac{\sigma}{\sqrt{n}}$, so $z=2.326$.” …
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