# STATGU5205Homework3 sol.pdf - STAT GR5205 Homework 3[100...

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STAT GR5205 Homework 3 [100 pts]Due 6:10 pm Thursday, October 20thProblem 1[25 pts]Consider the modelYi=μ+ii= 1,2, . . . , niiidN(0, σ2).The sample mean and sample variance are defined respectively as¯Y=1nnXi=1YiandS2Y=1n-1nXi=1(Yi-¯Y)2.Use Theorem (3.6) on Page 87 to prove that the sample mean¯Yand sample varianceS2Yare independent random variables.
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Problem 2[55 pts]Consider thesingle factor anova modelwith three groups. The three groups are drug dose1, drug dose 2 and control. Letn1and ¯y1respectively denote the number of respondentsand sample mean response for drug dose 1 group. Letn2and ¯y2respectively denote the