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3. Scientists conducted a half fractional factorial experiment involving factors A, B and C using the generator C=AB. Summary data are given below. Treatment Treatment Treatment Treatment Responses Sample Size Sample Mean Sample Variance C 88.8, 94.4, 82.1 3 87.7 42.72 a 69.6 69.6 NA b 30.6, 42.4, 32.6 W H 35.2 39.88 abc 83.2 1 83.2 NA Notice that the treatments in the table are in (Yates) standard order if we ignore "c". Yates algorithm produces the following values (p=3, q=1, p - q = 2 cycles): Treatment Means Cycle 1 Cycle 2 Fitted Effect C 87. 7 157 .3 275. 7 68 . 925 a 69 . 6 118 . 4 29.9 7. 475 b 35 . 6 -18.1 -38 . 9 -9. 725 abc 83 . 2 48 66 . 1 16 .525 Also note that treatments b and c were each replicated 3 times. This means that we can compute r(a) which we can use to determine which fitted effects are significant. Set the significance level at a=0.01. a. Perform some calculations to show that r(0.01) = 12.079. b. The defining relation in this experiment is I=ABC. Use this and r(0.01)=12.079 to determine which fitted effects are significant at the a=0.01 level. Just fill in the blanks in the table below to complete this exercise. Significant? Enter YES Fitted Effect Sum of Effects Estimated or NO below. 7.475 -9.725 16.525 c. If all interactions are negligible, which of factors A, B and C are most important