Propose a pivotal quantity and construct a 95% confidence interval. Please see the problem below.

Let X1,X2, "\"an be a random sample from N(ux,0x2), and let Y1,Y2, ...,Yn2 be a random sample from N (My, 03,2). Further, assume that the two random samples (X's and Y's) are independent. Suppose the computed sample variances are 5,} and 53,2. Consider estimating the ratio of the two population variances, that is: :i: y Propose a pivotal quantity and use this to derive and construct a 95% level equal 2 tails probability confidence interval for % . y (n1)32 Hint: Recall 02 ~x2(n_1). Also, recall the relationship of two independent Chi- Square distributed random variables to a F distributed random variable