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Three different design configurations are being considered for a particular component. There are four possible failure modes for the component. An engineer obtained the following data on number of failures in each mode for each of the three configurations. configuration appear to have an effect on type of failure? 1 Configuration 2 3 USE SALT State the appropriate hypotheses. O Hot Py = Ho: PPrPj i=1, 2, 3; j = 1, 2, 3, 4 H: at least one PP₁ Py O Ho: Py*P₁. P. i=1, 2, 3; j = 1, 2, 3, 4 H₁: at least one p = Pr Pj Pi P. H: at least one p O Ho: Pu P Failure Mode 1 2 3 4 20 44 17 9 4 17 7 12 12 31 14 5 1, 2, 3; j = 1, 2, 3, 4 i= 1, 2, 3; j = 1, 2, 3, 4 Pr P.j H: at least one P = Compute the test statistic value. (Round your answer to three decimal places.) x² = What can you say about the P-value? OP-value < 0.005 O 0.005 < P-value < 0.01 O 0.01 < P-value < 0.025 O 0.025 < P-value < 0.05 O 0.05 < P-value < 0.10 OP-value> 0.10

Three different design configurations are being considered for a particular component. There are four possible failure modes for the component. An engineer obtained the following data on number of failures in each mode for each of the three configurations. configuration appear to have an effect on type of failure? 1 Configuration 2 3 USE SALT State the appropriate hypotheses. O Hot Py = Ho: PPrPj i=1, 2, 3; j = 1, 2, 3, 4 H: at least one PP₁ Py O Ho: Py*P₁. P. i=1, 2, 3; j = 1, 2, 3, 4 H₁: at least one p = Pr Pj Pi P. H: at least one p O Ho: Pu P Failure Mode 1 2 3 4 20 44 17 9 4 17 7 12 12 31 14 5 1, 2, 3; j = 1, 2, 3, 4 i= 1, 2, 3; j = 1, 2, 3, 4 Pr P.j H: at least one P = Compute the test statistic value. (Round your answer to three decimal places.) x² = What can you say about the P-value? OP-value < 0.005 O 0.005 < P-value < 0.01 O 0.01 < P-value < 0.025 O 0.025 < P-value < 0.05 O 0.05 < P-value < 0.10 OP-value> 0.10

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 31EQ
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Three different design configurations are being considered for a particular component. There are four possible failure modes for the component. An engineer obtained the following data on number of failures in each mode for each of the three configurations. Does the configuration appear to have an effect on type of failure? State the appropriate hypotheses. 1 Configuration 2 3 O Ho: Pij USE SALT = Ho: Pij = P₁. P.j i=1, 2, 3; j = 1, 2, 3, 4 H₂: at least one Pij Pi. • P.j O Ho: Pij Ho: Pij P₁.P.j i = 1, 2, 3; j = 1, 2, 3, 4 H₂: at least one Pij = P₁. P.j Pi. P.j H₂: at least one Pij * Pi. P.j Ha: at least one Pij Failure Mode 3 17 1 20 4 12 i = 1, 2, 3; j = 1, 2, 3, 4 P₁. P.j i = 1, 2, 3; j = 1, 2, 3, 4 P₁ P.j 2 44 17 31 14 What can you say about the P-value? O P-value < 0.005 O 0.005 < P-value < 0.01 O 0.01 < P-value < 0.025 O 0.025 < P-value < 0.05 O 0.05 < P-value < 0.10 OP-value > 0.10 4 9 7 12 5 Compute the test statistic value. (Round your answer to three decimal places.) x² =
Transcribed Image Text:Three different design configurations are being considered for a particular component. There are four possible failure modes for the component. An engineer obtained the following data on number of failures in each mode for each of the three configurations. Does the configuration appear to have an effect on type of failure? State the appropriate hypotheses. 1 Configuration 2 3 O Ho: Pij USE SALT = Ho: Pij = P₁. P.j i=1, 2, 3; j = 1, 2, 3, 4 H₂: at least one Pij Pi. • P.j O Ho: Pij Ho: Pij P₁.P.j i = 1, 2, 3; j = 1, 2, 3, 4 H₂: at least one Pij = P₁. P.j Pi. P.j H₂: at least one Pij * Pi. P.j Ha: at least one Pij Failure Mode 3 17 1 20 4 12 i = 1, 2, 3; j = 1, 2, 3, 4 P₁. P.j i = 1, 2, 3; j = 1, 2, 3, 4 P₁ P.j 2 44 17 31 14 What can you say about the P-value? O P-value < 0.005 O 0.005 < P-value < 0.01 O 0.01 < P-value < 0.025 O 0.025 < P-value < 0.05 O 0.05 < P-value < 0.10 OP-value > 0.10 4 9 7 12 5 Compute the test statistic value. (Round your answer to three decimal places.) x² =
State the conclusion in the problem context. (Use a = 0.05.) O Fail to reject Ho. There is no evidence that configuration has a significant effect on type of failure. Fail to reject Ho. There is evidence that configuration has a significant effect on type of failure. Reject Ho. There is evidence that configuration has a significant effect on type of failure. Reject Ho. There is no evidence that configuration has a significant effect on type of failure. You may need to use the appropriate table in the Appendix of Tables to answer this question.
Transcribed Image Text:State the conclusion in the problem context. (Use a = 0.05.) O Fail to reject Ho. There is no evidence that configuration has a significant effect on type of failure. Fail to reject Ho. There is evidence that configuration has a significant effect on type of failure. Reject Ho. There is evidence that configuration has a significant effect on type of failure. Reject Ho. There is no evidence that configuration has a significant effect on type of failure. You may need to use the appropriate table in the Appendix of Tables to answer this question.
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