2. An inspector samples cans from a truckload of canned creamed corn to estimate the total number of worm fragments in the truckload. The truck has 580 cases; each case contains 24 cans. The inspector samples 12 cases at random, and subsamples 3 cans randomly from each selected case. Case (psu) ssu 1 2 3 5 8 9 10 11 12 ------- Can 1 1 4 0 3 3 Can 2 5 2 7 Can 3 Estimate the total number of worm fragments, along with a 95% CI. Note: This is two-stage cluster sample with N = 580, n = 12, M = 24, and m = 3. a) The y,[i =1:12]= 4.3 3.3 1.0 5.0 7.0 3.3 3.7 1.7 5.0 2.7 6.7 0.0. Compute i, and f. [Hint: f, = My, and f = -i, . Note y, =-Ey, for each psu from 1 to 12. ] b) Compute s, = _ _(, -1) c) Compute V's, = [M'(1- m) given s, [i = 1:12]=9.3 1.3 1.0 3.0 7.0 12.3 5.3 2.3 4.0 2.3 6.3 0.0 [Hint : In Excel, put the s, in column A and multiply column A by -(1 -- to get column B. Then sum column B. Note: s/ =- _(v, -y,)' for each psu. ] d) Compute Vy = (1 - 1) S; e) Compute V(i) = N'Vy +-V, and SE(1) = \\V(i) f) Look up the for in Table A.4 on row 11 (Degrees of freedom 12-1 = 11) and column 0.025. Then compute the confidence interval for f: i -tan SE(i) Stsi+tana SE(i)