Dr. Hackney STA Solutions pg 139

# Dr. Hackney STA Solutions pg 139 - 8-18Solutions Manual for...

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Unformatted text preview: 8-18Solutions Manual for Statistical Inferencec. Using the values in Exercise 8.41d, we obtainT=-1.46 and ˆν= 20.64. So the p-value is.16. There is no evidence that the mean age differs between the core and periphery.d.F=S2X/S2Y= 3.36. Comparing this with anF13,8distribution yields a p-value of 2P(F≥3.36) =.09. So there is some slight evidence that the variance differs between the core andperiphery.8.43 There were typos in early printings. Thetstatistic should be(¯X-¯Y)-(μ1-μ2)q1n1+ρ2n2q(n1-1)s2X+(n2-1)s2Y/ρ2n1+n2-2,and theFstatistic should bes2Y/(ρ2s2X). Multiply and divide the denominator of thetstatisticbyσto express it as(¯X-¯Y)-(μ1-μ2)qσ2n1+ρ2σ2n2divided bys(n1-1)s2X/σ2+ (n2-1)s2Y/(ρ2σ2)n1+n2-2.The numerator has a n(0,1) distribution. In the denominator, (n1-1)s2X/σ2∼χ2n1-1and(n2-1)s2Y/(ρ2σ2)∼χ2n2-1and they are independent, so their sum has aχ2n1+n2-2distribution....
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