Download Homework 8 Solutions | Statistics for Engineering | STAT 4706 and more Assignments Statistics in PDF only on Docsity! Stat 4706 HW 8/9 Solutions 1) Two factors are though to influence the deposition rate (in seconds) for a pulse laser to deposit one monolayer of material. A 22 design was run with spot size (50 or 60 mm) and laser energy (1.5 or 2.0 J/cm2) as the factors. a) Indicate which levels of the factor (low or high) are being observed for each of the treatment combinations below. Treatment Combination Replicate 1 Replicate 2 Level of Factor A Level of Factor B (1) 8.34 7.44 a 5.20 4.96 b 7.01 7.09 ab 4.45 4.70 b) Identify the model for y that this experimental design represents. c) Generate an interaction plot (by hand or computer). Based on the graph, does there seem to be an interaction effect? How do you know? d) Calculate an estimate for each of the effects (by hand). e) Use an ANOVA procedure to determine which effects are significant (by hand). SSTotal = ( ) N y y 2 2 ∑∑ − SSError = SSTOTAL – (SSA + SSB+ SSAB) Degrees of Freedom: dfA = 1 dfB = 1 dfAB = 1 dfTOTAL = N-1 dfError = dfTOTAL – (dfA + dfB+ dfAB) Mean Squares: MSA = SSA/dfA MSB = SSB/dfB MSAB = SSAB/dfAB MSError = SSError/dfError 2) An engineering student wanted to know which factors influence the time (in seconds) for his car to go from 0 to 30 to 0 miles per hour. Factor A was the launch, which was either with no wheel spin (low) or dropping the clutch at 2500 rpm (high). Factor B is either stopping with the transmission in neutral (low) or in second gear (high). Factor C is the air conditioning off (low) or on (high). a) Indicate the model that this experimental design represents. Factor A Factor B Factor C Time (n=2 replicates) Variance Treatment combination Low Low Low 9.43, 9.34 .00405 High Low Low 8.80, 8.52 .0392 Low High Low 9.17, 9.15 .0002 Low Low High 9.87, 9.66 .02205 High High Low 8.36, 8.43 .00245 High Low High 8.81, 8.92 .00605 Low High High 9.56, 8.94 .1922 High High High 8.40, 8.46 .0018 b) Indicate the treatment combination that each row indicates, (1), a, b, etc., in the table above. (see above) c) Complete t-tests to determine which factors are significant (by hand). Pooled Variance: ∑ = ∧ ∧ = k i k i 2 1 2 2 2 σσ = .0335 SE(Effect) = =− ∧ 2 2 2kn σ .091515 H0: Effect is not significant. H1: Effect is significant. Test Statistics: d) Indicate the final model for y that this experiment represents using significant terms only. e) Using only the significant effects, find a regression model and predict y when both factor A and B are at low levels and C is at the high level.
