CAIE FP2 2013 June — Question 8

Exam BoardCAIE
ModuleFP2 (Further Pure Mathematics 2)
Year2013
SessionJune
TopicLinear combinations of normal random variables
TypeStandard CI with summary statistics

8 The number, \(x\), of a certain type of sea shell was counted at 60 randomly chosen sites, each one metre square, along the coastline in country \(A\). The number, \(y\), of the same type of shell was counted at 50 randomly chosen sites, each one metre square, along the coastline in country \(B\). The results are summarised as follows. $$\Sigma x = 1752 \quad \Sigma x ^ { 2 } = 55500 \quad \Sigma y = 1220 \quad \Sigma y ^ { 2 } = 33500$$ Find a 95\% confidence interval for the difference between the mean number of sea shells, per square metre, on the coastlines in country \(A\) and in country \(B\).