exam2-fall06 - Exam 2 Statistics 426 13 Dec 2006...

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Exam 2: Statistics 426. 13 Dec, 2006 Announcement: The exam carries 40 points but the maximum possible score is 35. (1) Suppose that X 1 , X 2 , . . . , X n are i.i.d Unif( - θ - 2 , θ - 2 ) for some θ > 0. Find a MOM estimate for θ and the MLE of θ based on the X i ’s. (8) (2) Consider i.i.d. data { X i , Y i } n i =1 where X i is the blood–pressure of indiviudal i before taking a drug and Y i is the blood–pressure of the same individual after being on the drug. It may be assumed that X i N ( μ 1 , σ 2 ) and Y i N ( μ 2 , σ 2 ) for some unknown σ and that the correlation between X i and Y i is some (unknown) positive fraction ρ . Of interest is the difference in blood–pressure μ 1 - μ 2 . (i) How can you use the difference in observed blood pressures: the X i - Y i ’s, to construct a level 1 - α confidence interval for the quantity of interest? (ii) Suppose now that the doctor wants a lower confidence limit on the difference of mean blood–pressures – i.e. a number a such that the chance that the difference in mean blood pressures
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