ST512 Quiz 2 SSII-2010 1. A poultry scientist was studying various dietary additives to increase the rate at which chickens gain weight. One of the potential additives was studied by creating a new diet which consisted of a standard basal diet supplemented with varying amounts of the additive (0, 20, 40, 60, 80, 100). There were sixty chicks available for the study. Each of the six diets was randomly assigned to ten chicks. At the end of four weeks, the feed efficiency ratio, feed consumed (gm) to weight gain (gm), was obtained for the sixty chicks. An analysis of variance table is presented below with the estimated coefficients for the corresponding linear model. Class Level Information Class Levels Additive Values 6 0 20 40 60 80 100 Number of Observations Read Number of Observations Used 60 60 Dependent Variable: FeedEffRatio Source DF Sum of Squares Mean Square Model 5 66.85993333 13.37198667 Error Pr > F <.0001 1.63990000 Corrected Total 59 R-Square Coeff Var Root MSE FeedEffRatio Mean 0.976060 6.272309 0.174266 2.778333 Parameter Intercept Additive Additive Additive Additive Additive Additive Let F Value Estimate 0 20 40 60 80 100 4.790000000 -3.349000000 -2.596000000 -2.418000000 -2.237000000 -1.470000000 0.000000000 B B B B B B B Standard Error t Value Pr > |t| 0.05510764 0.07793397 0.07793397 0.07793397 0.07793397 0.07793397 . 86.92 -42.97 -33.31 -31.03 -28.70 -18.86 . <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 . y0 , y 20 , y 40 , y 60 , y80 , y100 denote the sample treatment means. (A) Fill in blanks in above table of Analysis of Variance. (B) Write the lineal model for this experiment. (C) Compute, if possible, the t test associated with y 0 - y100 t= ________. (D) Compute y 40 = _______ and its standard error = _________. (E) Write the predicted value for FeedEffRatio when Additive level of 60. July 22, 2010 Page 1 ST512 Quiz 2 SSII-2010 (F) The graph plot of the least squares means is presented next, with leverage and Cook’s D plots for residual checking and validation of the Anova Assumptions. Please write a few lines with your findings after inspecting these graphs. July 22, 2010 Page 2 ST512 2. Quiz 2 SSII-2010 I have a completely randomized design with 3 treatments (drug A, B, and C) and 5 replicates of each. Here are some sums of squares (SSq) and F tests for some contrasts: A versus B SSq = 22.5 F = 4.5 B versus C SSq = 202.5 F = 40.5 A vs. avg. of B,C SSq = 187.5 F = ____ C vs. avg. of A,B SSq = _____ (A) Compute the treatment sum of squares. (B) Fill in blanks 3. 4. Give an example of a one-way ANOVA (Completely Randomized design), indicating: i. Response, ii. treatment factor, iii. experimental units, iv. number of repetitions, v. Error Df, and vi. (Research) Question of interest, why do you run this experiment? Please comment the following form Cottingham et al. paper July 22, 2010 Page 3