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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.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 93E
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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.
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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