Question

f) (5 marks) Carry out the most appropriate test to determine if there are any significant differences in the mean velocity among the 8 different groups? SHOW ALL STEPS. Use a 5% significance level. g) (5 marks) What is the overall effect of ring (with O-ring vs. without O-ring) on the mean of velocity? First, define a linear contrast that will define the overall effect of ring on mean velocity. Then, calculate a 95% confidence interval for this effect. SHOW ALL STEPS. Based on this confidence interval, does it appear that there is a difference in mean velocity with vs. without an O-ring? h) (6 marks) For this part, consider the three models defined below and use the three tables of computer output analyzing those three models. Carry out the most appropriate test to determine if there are any differences in the me an velocity for the four different levels of the discharge hole area, after accounting for the volume and whether or not an O-ring is included. SHOW ALL STEPS. Use a 1% significance level. Model 1: μ(velocity (area)-A, + β,d\ + β,d2 + β,d, Model 2: u(velocity volume,ring)-P +Bvolume+A.with Model 3: μ(velocity \ volume,ring, area-B + β.volume + β.with + β,dı + β,d 2 + β,d : ANOVA Sum of df re Regression Residual Total 3534.206 38289.739 51823.944 a. Predictors: (Constan), D3, D2, D1 b. Dependent Variable: Velocty ANOVA table for model 2: ANOVA Sum of df Mean Square Si Regression Residual Total Squares 32157.352 19666.592 1823.944 a. Predictors: (Constan), with Volume b. Dependent Variable: Velocity ANOVA table for model 3: ANOVA Sum of df Mean Square Si Regression Residual Total 45691.558 6132.387 51823.94 a. Predictors: (Constan), with Volume, D3, D2, D1 b. Dependent Variable: Velocity

Answer 1

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