mid19f-324.pdf - Name: ID # McGill University STATISTICS...

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Name:ID #McGill UniversitySTATISTICS (MATH324)Mid-Term Exam, Tuesday October 22nd, 2019Time: 11:30 - 13:00Instructions:This test consists of four questions.There is no optionalquestion.Please answer all four questions.A two-sided 8.5×11 page offormula and a calculator are permitted. The following information may beof use to you:XNormal(μ, σ2) :fX(x) =12πe-(x-μ)22σ2xRXPoisson(λ) :pX(x) =e-λλxx!,x∈ {0} ∪NXBinomial(n, p) :pX(x) =nxpx(1-p)n-x,x= 0,1,· · ·, nBernoulli(p) = Binomial(1, p)ForZN(0,1),P(|Z|<1.96) = 0.95.Good luck.1
Question 1.In polycrystalline aluminum, the number of grain nucle-ation sites per unit volume is modelled as having a Poisson distributionwith meanλ. Fifty unit-volume test specimens subjected to annealing underregime A produced an average of 20 sites per unit volume. Fifty indepen-dently selected unit-volume test specimens subjected to annealing regime Bproduced an average of 23 sites per unit volume.(a)Estimate the difference in the mean numbers of nucleation sitesλA-λBfor regimes A and B, and find a 95% confidence interval for it.(5 marks)

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