Dr. Hackney STA Solutions pg 131

Dr. Hackney STA Solutions pg 131 - 8-10Solutions Manual for...

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Unformatted text preview: 8-10Solutions Manual for Statistical Inferenceb. The size is.05 =() = 1 + (-c)-(c) which impliesc= 1.96. The power (1-type II error) is.75(+) = 1 + (-c-n)-(c-n) = 1 + (-1.96-n)|{z}-(1.96-n).(-.675).25 implies 1.96-n=-.675 impliesn= 6.9437.8.19 The pdf ofYisf(y|) =1y(1/)-1e-y1/,y >.By the Neyman-Pearson Lemma, the UMP test will reject if12y-1/2ey-y1/2=f(y|2)f(y|1)> k.To see the form of this rejection region, we computeddy12y-1/2ey-y1/2=12y-3/2ey-y1/2y-y1/22-12which is negative fory <1 and positive fory >1. Thusf(y|2)/f(y|1) is decreasing fory1and increasing fory1. Hence, rejecting forf(y|2)/f(y|1)> kis equivalent to rejecting forycoryc1. To obtain a sizetest, the constantscandc1must satisfy=P(Yc|= 1) +P(Yc1|= 1) = 1-e-c+e-c1andf(c|2)f(c|1)=f(c1|2)f(c1|1).Solving these two equations numerically, for=.10, yieldsc=.076546 andc1= 3.637798....
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This note was uploaded on 02/03/2012 for the course STA 1014 taught by Professor Dr.hackney during the Spring '12 term at UNF.

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