Question 2 (16 points ) A chemist wishes to test the effect of four chemical agents on the strength of a particular type of cloth . Because there might be variability from one bolt to another , the chemist decides to use a randomized block design , with the bolts of cloth considered as blocks . She selects five bolts randomly from a population of bolts and applies all four chemicals in random order to each bolt . The resulting tensile strengths follow A snippet of the data and the R output for data analysis are given below . # # Chemical Bolt Strength # # 1 1 73 # # 2 68 W N # # 3 74 # # 4 71 # # 5 67 # # 6 73 # # 7 2 67 # # 8 75 # # 9 4 *# 10 IF W WW WWNNNNNET # # 11 # # WNH # # 13 # # 14 4 73 # # 15 68 # # 16 73 # # 17 71 *# 18 75 # # 19 75 # # 20 aggregate (dat_chem $Strength list (dat_chem $ Chemical ) , mean ) # # Group . 1 X # # 1 1 70.6 # # 2 2 71.4 # # 3 3 72.4 ## 4 4 72.6 summary (aov (Strength ~Bolt + Chemical , data =dat_chem ) ) # # Df Sum Sq Mean Sq F value Pr (> F) # # Bolt 4 157.00 39 . 25 21 . 606 2. 06e -05 * * * # # Chemical 3 12.95 4.32 2.376 . 121 # # Residuals 12 21 . 80 1.82 # # ## Signif . codes : 0 * ** 0.001 * * 0.01 0. 05 0. 1 confint (1mer (Strength ~ 1 . Chemical ( 1 | Bolt ) , contrasts =list (Chemical =contr . sum (4 ) ) , data =dat_chem ) ) ## Computing profile confidence intervals . . . # # 2.5 % 97 .5 % # # . sigo1 1. 5581595 6. 0750788 # # . sigma 0. 8755784 1. 8094874 # # (Intercept ) 68. 7375597 74. 7624366 # # Chemical1 2. 1269554 - 0. 1730446 # # Chemical2 - 1. 3269554 0. 6269554