Question

Three different design configurations are being considered for a particular component. There are two possible failure modes for the component. An engineer obtained the following data on the number of failures in each mode for each of the three configurations. Is there evidence to conclude that the configuration has an effect on the type of failure?
Failure Mode
1 2 3 4
Configuration 1 20 44 17 9
2 4 17 7 12
3 10 31 14 5

Answer 1

Answer:

No evidence .because the configurations factors and failure mode are independent

Step-by-step explanation:

Determine if there is sufficient evidence to conclude that configuration affects the type of failure

Number of configurations = 3

Number of failures = 4

assuming Pij represents proportion of items in pop i of the category j

H0 : Pij = Pi * Pj,  I = 1,2,-- I,  j = 1,2,---J

Hence the expected frequencies will be

16.10 , 43.58 , 18, 12.31

7.5,  19.37, 8 , 5.47

10.73, 29.05, 12, 8.21

x^2 = 13.25

test statistic = 14.44. Hence the significance level where Null hypothesis will be acceptable will be = 2.5%