Suppose that X1,...,X11 form a random sample from the normal distribution with unknown mean 1 and unknown variance 2 1 . Suppose also that Y1,...,Y21 form an independent random sample from the normal distribution with unknown mean 2 and unknown variance 2 2 . Suppose that we wish to test the hypotheses in Eq. (9.7.7). Let be the equal-tailed two-sided F test with level of significance 0 = 0.5. a. Compute the power function of when 2 1 = 1.012 2 . b. Compute the power function of when 2 1 = 2 2 /1.01. c. Show that is not an unbiased test. (You will probably need computer software that computes the function Gm1,n1. And try to minimize the amount of rounding you do.)

#data analysis using hamilton data to predict y data=read.csv("hamilton.csv") #wewill check the performance of first-order model m1=lm(y~x1+x2, data) summary(m1) par(mfrow=c(1,3)) plot(data[,1], m1$res) plot(data[,2],m1$res) plot(fitted(m1),m1$res) #I did not observe an obvious pattern in the residual plots #we will present the partial residual plots on x1 partial=m1$res+coef(m1)[2]*data[,1]...