5.1 Four chemicals were used to combat plant lice on sugar beets, each chemical being applied to one plot. Twenty-five leaves were picked from each plot, and the number of plant lice on each leaf was recorded. The data obtained were as follows: Chemical 1 2 3 4 5 6 7 8 9 10 11 12 13 I 12 13 26 13 17 24 14 10 6 4 2 10 8 FEN II 10 21 34 15 5 22 12 25 18 12 2 2 10 III 23 14 14 20 27 25 17 18 29 14 31 5 13 IV 32 26 24 16 32 18 33 16 34 18 9 19 29 Chemical 14 15 16 17 18 19 20 21 22 23 24 25 I 6 7 13 18 10 18 3 4 18 13 10 21 II 22 17 20 19 20 12 11 16 5 11 17 16 III 18 23 16 13 23 4 16 17 9 28 23 19 IV 30 18 25 20 21 27 31 25 33 24 16 24 Preliminary calculations gave the following 0 Chemical (-Y)² I 300 4600 28.409 II 374 6922 5.6179 III 459 9603 1.061 15 IV 600 15490 44.489 4 25 (Yi. ΣΣ (Υ, - 7.) - 6582.110 1-11-1 Assume that Y,,+a,+, where Σ-a,-0 and e,,IND(0, 2). (a) Fill in an analysis of variance table and test at a .05 level whether differences exist among the four chemicals. (b) Write down point estimates of the following parameters: -M-M-1 (1) The overall mean number of plant lice per leaf for the four chemicals. (ii) +a₁, the mean for the first chemical. (iii) α₁-α. (iv) a-(a₂+a, + a₁)/3. (^) (c) Obtain confidence intervals with an overall 95% level for the quantities, +α, α-a₂, and a₁-(a₂+ a,+ a)/3 using the multiple tech- nique. (d) Obtain confidence intervals for a₁-a, a₁-a, and a₁-α using Sheffé's technique. (e) Obtain a 95% confidence interval for 2.