The article "Optimization of Surface Roughness in Drilling Using Vegetable-Based Cutting Oils Developed from Sunflower Oil+ gave the following data on x₂ = spindle speed (rpm), x₂ = feed rate (mm/rev), x = drilling depth (mm), and y = surface roughness (um) when a semisynthetic c fluid was used. X1 X2 x3 e* y 320 0.10 15 2.27 -1.32 320 0.12 20 4.14 1.08 320 0.14 25 4.69 0.26 1 420 0.10 20 1.92 -0.40 420 0.12 25 2.63 -0.79 4.34 0.99 420 0.14 15 520 0.10 25 2.03 1.64 520 0.12 15 2.34 0.03 520 0.14 20 2.67 -1.52 (a) Here is partial Minitab output from fitting the model with x₁, x₂, and x3 as predictors (authors of the cited article used Minitab for this purpose). SE Coef 1.871 0.002231 11.16 0.04463 0.546589 R-Sq 83.9% R-Sq(adj) Predictor Constant O Ho: P3-0 H₂: 8₂ 50 ⒸH: 83-0 *1 x₂ x₂ s Does drilling depth provide useful information about roughness given that spindle speed and feed rate remain in the model? (Use a = 0.05.) State the appropriate hypotheses. O Ho: P3=0 H₂: P₂ <0 ⒸHg: 13=0 Coef 0.099 -0.006767 45.67 0.01333 State the appropriate test statistic and P-value from the output above. to P-value= T P 0.05 0.960 -3.03 0.029 4.09 0.009 0.30 0.777 74.2% State the conclusion in the problem context. O Reject H. Drilling depth does not appear to provide useful information about roughness, given that spindle speed and feed rate remain in the model. O Reject H. Drilling depth appears to provide useful information about roughness, given that spindle speed and feed rate remain in the model. O Fail to reject Ho. Drilling depth does not appear to provide useful information about roughness, given that spindle speed and feed rate remain in the model.
The article "Optimization of Surface Roughness in Drilling Using Vegetable-Based Cutting Oils Developed from Sunflower Oil+ gave the following data on x₂ = spindle speed (rpm), x₂ = feed rate (mm/rev), x = drilling depth (mm), and y = surface roughness (um) when a semisynthetic c fluid was used. X1 X2 x3 e* y 320 0.10 15 2.27 -1.32 320 0.12 20 4.14 1.08 320 0.14 25 4.69 0.26 1 420 0.10 20 1.92 -0.40 420 0.12 25 2.63 -0.79 4.34 0.99 420 0.14 15 520 0.10 25 2.03 1.64 520 0.12 15 2.34 0.03 520 0.14 20 2.67 -1.52 (a) Here is partial Minitab output from fitting the model with x₁, x₂, and x3 as predictors (authors of the cited article used Minitab for this purpose). SE Coef 1.871 0.002231 11.16 0.04463 0.546589 R-Sq 83.9% R-Sq(adj) Predictor Constant O Ho: P3-0 H₂: 8₂ 50 ⒸH: 83-0 *1 x₂ x₂ s Does drilling depth provide useful information about roughness given that spindle speed and feed rate remain in the model? (Use a = 0.05.) State the appropriate hypotheses. O Ho: P3=0 H₂: P₂ <0 ⒸHg: 13=0 Coef 0.099 -0.006767 45.67 0.01333 State the appropriate test statistic and P-value from the output above. to P-value= T P 0.05 0.960 -3.03 0.029 4.09 0.009 0.30 0.777 74.2% State the conclusion in the problem context. O Reject H. Drilling depth does not appear to provide useful information about roughness, given that spindle speed and feed rate remain in the model. O Reject H. Drilling depth appears to provide useful information about roughness, given that spindle speed and feed rate remain in the model. O Fail to reject Ho. Drilling depth does not appear to provide useful information about roughness, given that spindle speed and feed rate remain in the model.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:The article "Optimization of Surface Roughness in Drilling Using Vegetable-Based Cutting Oils Developed from Sunflower Oil" + gave the following data on x₂ = spindle speed (rpm), x₂ = feed rate (mm/rev), x3 = drilling depth (mm), and y = surface roughness (μm) when a semisynthetic cutting
fluid was used.
e*
X1 X2 x3 y
320 0.10 15 2.27 -1.32
320 0.12 20 4.14 1.08
320 0.14 25 4.69 0.26
420 0.10 20
1.92 -0.40
420 0.12 25 2.63 -0.79
420 0.14 15 4.34 0.99
520 0.10 25 2.03 1.64
520 0.12 15 2.34 0.03
520 0.14 20 2.67 -1.52
(a) Here is partial Minitab output from fitting the model with x₁, x₂, and x3 as predictors (authors of the cited article used Minitab for this purpose).
Coef
0.099
-0.006767
45.67
SE Coef
1.871
0.002231
11.16
0.04463
T
P
0.05 0.960
-3.03 0.029
4.09 0.009
0.01333
0.30
0.777
0.546589 R-Sq 83.9%
R-Sq (adj) - 74.2%
Does drilling depth provide useful information about roughness given that spindle speed and feed rate remain in the model? (Use a = 0.05.)
State the appropriate hypotheses.
OHO: B3 = 0
Ha: P3 <0
Predictor
Constant
x₁
x₂
x₂
$
Ho: P3 = 0
Ha: P3>0
O Ho: P3=0
H₂:03 ≤0
O Ho: P3 = 0
Ha: P3"
State the appropriate test statistic and P-value from the output above.
t =
P-value=
#0
State the conclusion in the problem context.
O Reject H. Drilling depth does not appear to provide useful information about roughness, given that spindle speed and feed rate remain in the model.
O Reject H. Drilling depth appears to provide useful information about roughness, given that spindle speed and feed rate remain in the model.
O Fail to reject Ho. Drilling depth does not appear to provide useful information about roughness, given that spindle speed and feed rate remain in the model.
O Fail to reject Ho. Drilling depth appears to provide useful information about roughness, given that spindle speed and feed rate remain in the model.
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