PROBLEMS 5. 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: (00 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- 3/00 II 10 21 34 15 5 22 12 25 18 12 2 2 10 374 III 23 14 14 20 27 25 17 18 29 14 31 5 13-45 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 1-2-95 Preliminary calculations gave the following Chemical Y (-) I 300 4600 28.409 II 374 6922 5.617 III 459 9603 1.061 IV 600 15490 44.489 4 25 =79576 ΣΣ (Υ -Υ). -6582.110 1-11-1 [99] 32,022.28 ONE-WAY ANALYSIS OF VARIANCE Assume that Y,,+α, + &,,, where Σ-a,-0 and E, IND(0, 0²). (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: (i) The overall mean number of plant lice per leaf for the four chemicals, 1731 (ii) +a₁, the mean for the first chemical. (iii) a₁-α2.-7 (iv) a-(a2+ a3 + α₁₂)/3. (V) M & 2PM (c) Obtain confidence intervals with an overall 95% level for the quantities, +α, α-a₂, and a₁-(a₂+a+a4)/3 using the multiple tech- nique. " (d) Obtain confidence intervals for a₁-d2, a₁-a3, and a₁-α4 using Sheffé's technique. (e) Obtain a 95% confidence interval for o2. 5.2. Serum cholesterol was measured on 24 men whose ages were in the range 65 to 74 years. Classified by annual income, the values are as follows: Observation Income 1 2 3 4 5 6 7 8 9 10 < $8,000 229.5 228.3 209.3 240.4 214.1 240.1 210.5 218.8 223.4 217.6 $8,000-20,000 235.1 244.9 243.7 232.9 253.1 251.9 241.0 224.9 >$20,000 241.2 227.9 244.8 240.5 252.1 232.1 - -