Question

Each of J = 2 operators were asked to make K = 2 independent measurements on / = 10 injection-molded parts during production. A two-way-interaction ANOVA table for analyzing the data is given below. Responses were 0.001 mm above the nominal value of 685 mm. Source df SS MS F P-value A = Part 9 11750 1305.5 ? 6.06e-05 B = Operator 1 648 648.0 ? 0.0603 AB Interaction 9 2538 282.0 0.1484 Error 20 3269 163.5 Total 39 18205 Operator effect is fixed. Let B, be the main effect of Operator j. Complete the hypothesis test below. (12 pts] i. H: versus H : {H, is false.) ii. Ftest statistic = iii. Rejection Region (a = 0.05) = P-value = iv. Circle one: Reject Retain OLE A plot of mean is given on the right. Does this plot agree with the ANOVA results regarding the interactions between Parts and Operators? Explain briefly. [5 pts] Average Response 050 000 TTTTTT 1 10 2 3 4 5 6 7 8 9 Assume that Part effects are fixed. Compute w in the T Method (a = 0.05) for comparing levels of Part and use it to determine if Part 2 (X=-327.75) and Part 3 (X3 = -318.50) are statistically different. [8 pts)

Answer 1

() Ho : There is no significant difference. (1) test statistics = MSA - 1305.5-7.984 Msemor 163.5 (iii) Rejection Region = 2.392 , pralue= 6.06e-os civ Reject. For Bi- (i) Ho: There is no significant difference. (ii) F test = mSB = 648 = 3.96 msemor 163.5 (iii) Rejection Region = 4.351 , P-value = 0.0603 civ) Retain

For AB: i Hoi There is F test = is no significant difference. mSAB = 282.0 = 1.724 mshoror - 282.0 = 1.724 Region = 2.3928 , p-value = 0.1484 (171) civ Rejection Retain, from Interaction plat : Yes this plot agree with ANOVA results regarding the interactions between Parts and Operators because we see the interaction they mean lines of Ponts and Operators are not interacting. so we can say there is no interaction between Pants and operators.