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? 1 Configuration 2 3 USE SALT State the appropriate hypotheses. Pi. O Ho: Pij = i = 1, 2, 3; j = 1, 2, 3, 4 O Ho: Pij * Pi P.j Ho: Pij P₁.¹ P.; i = 1, 2, 3; j = 1, 2, 3, 4 H₂: at least one Pij = P₁. P.j Ha: at least one pij* Failure Mode 1 2 3 22 44 17 4 19 10 31 Pi. i=1, 2, 3; j = 1, 2, 3, 4 P.j H₂: at least one pij= Pj. P.j Ho: Pij = P₁. P.j = 1, 2, 3; j = 1, 2, 3, 4 H₂: at least one pij * Pi. P.j 4 9 7 12 5 14 Compute the test statistic value. (Round your answer to three decimal places.) x² =

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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?
O Ho: Pij
State the appropriate hypotheses.
Pi.
P.j
=
1
Configuration 2
3
=
USE SALT
O Ho: Pij
Ha: at least one Pij
#
i = 1, 2, 3; j = 1, 2, 3, 4
Ho: Pij * P₁. • P.j
Ha: at least one pij = P₁. • P.j
#
Pi.
P.j
= 1, 2, 3; j = 1, 2, 3, 4
P₁.
P.j
Ha: at least one Pij =
Failure Mode
1
2
3
44
17
22
4
19
10 31 14
i = 1, 2, 3; j = 1, 2, 3, 4
Pi.
P.j
O Ho: Pij = P₁. P.j i = 1, 2, 3; j = 1, 2, 3, 4
H₂: at least one Pij ‡ Pi. ' P.j
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? O Ho: Pij State the appropriate hypotheses. Pi. P.j = 1 Configuration 2 3 = USE SALT O Ho: Pij Ha: at least one Pij # i = 1, 2, 3; j = 1, 2, 3, 4 Ho: Pij * P₁. • P.j Ha: at least one pij = P₁. • P.j # Pi. P.j = 1, 2, 3; j = 1, 2, 3, 4 P₁. P.j Ha: at least one Pij = Failure Mode 1 2 3 44 17 22 4 19 10 31 14 i = 1, 2, 3; j = 1, 2, 3, 4 Pi. P.j O Ho: Pij = P₁. P.j i = 1, 2, 3; j = 1, 2, 3, 4 H₂: at least one Pij ‡ Pi. ' P.j 4 9 7 12 5 Compute the test statistic value. (Round your answer to three decimal places.) x²
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