02 (15 points) Suppose X1, , Xm is a random sample from Normalmx, 0%) distribution and Yl , , Y" is another independent random sample from N ormalmy, 0,2,) distribution. Further, suppose ,uX, ,uy, x and 07 are all unknown parameters, and that we wish to construct a 100(1 00% confidence interval for the ratio 2 "_Y 2. 6X of variances, (a) Explain (in steps) how you would use the F distribution described above to construct an exact 2 \"Y 100(1 a)% confidence interval for the ratio of variances, 2,- 5X (b) A random sample of m = 46 golden delicious apples taken from a tree were weighed, and their mean was found to be it = 186 (grams) and the standard deviation was found to be s = 16.2 (grams). In addition, another independent sample of n = 32 mutsu apples were taken from a tree and were weighed with their mean as )7 = 215 (grams) and their standard deviation as sy = 25.1 (grams). Assuming that the samples came from N ormal(,uX, 6;) and N 0rmal(;ry, 612,) distributions, respectively, obtain a 95% 2 . . . . CT . confidence Interval for the ratio of variances, :. For this purpose, you may use the values of the lower \"X and upper 2.5% points of F -distribution with (v1, v2) = (45, 31) degrees of freedom given by 0.5287 and 1.9688, respectively; (c) Comment on what you observe from this 95% confidence interval