# hw4_sol.pdf - Q1 solution To use the Yate’s algorithm...

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3 Q1 solution To use the Yate’s algorithm, make sure to put the design table into standard order first, then apply the Yate’s algorithm A B C y (1) (2) (3) Divisor Estimation Label - - - 60 121 250 499 2 k =8 62.375 mean + - - 61 129 249 45 2 k -1 =4 11.25 A - + - 54 119 22 19 2 k -1 =4 4.75 B + + - 75 130 23 37 2 k -1 =4 9.25 AB - - + 58 1 8 -1 2 k -1 =4 -0.25 C + - + 61 21 11 1 2 k -1 =4 0.25 AC - + + 55 3 20 3 2 k -1 =4 0.75 BC + + + 75 20 17 -3 2 k -1 =4 -0.75 ABC Q2 solution Factor A: time (12 h - 1”, 18h “+1”) ; Factor B: culture (medium 1 - 1”, medium 2 “+1”) Mean A B AB y i1 y i2 y i3 y i4 y i5 y i6 i y 2 i S + - - + 21 22 23 28 20 26 23.333 9.467 + - + - 25 26 24 25 29 27 26 3.2 + + - - 37 39 38 38 35 36 37.167 2.167 + + + + 31 34 29 33 30 35 32 5.6 divisor 4 2 2 2 1. Mean and effect calculation Grand mean = (23.333+26+37.167+32)/4=29.625 Main effect A= (-23.333-26+37.167+32)/2=9.917 Main effect B= (-23.333+26-37.167+32)/2=-1.25 Interaction effect AB= (23.333-26-37.167+32)/2=-3.917 2. Then calculate the overall error variance, 4 2 2 1 1 5.108 4 i i S S = = = Standard error 2 1 1 ( ) 5.108 24 24 SE mean S = = = 0.461 2 4 4 ( ) 5.108 24 24 SE effect S = = = 0.922 95% confidence interval /2, ( ) N p effect t SE effect /2, 0.025,24 4 0.025,20 2.086 N p t t t = = = Estimation Half width of 95% C.I. /2, N p t SE Significant? Mean 29.625 0.962 Yes A 9.917 1.923 Yes B 1.25 1.923 AB -3.917 1.923 Yes

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