LetX1,...,Xnbe a random sample from theN(µ1,s12) distribution, and let Y1,...,Ymbe a random sample from theN(µ2,s2) distribution. Assume that the two random sam- ples are independent of each...

LetX1,...,Xnbe a random sample from theN(µ1,s12) distribution, and let Y1,...,Ymbe a random sample from theN(µ2,s2) distribution. Assume that the two random sam- ples are independent of each other.(a)Find a pivotal quantity that involvess12ands2, but notµ1 orµ2. (Hint: The pivotal quantity should have anFdistribution.)(b)Using the pivotal quantity from part (a), find a 95% confidence interval fors12/s2.