Question

Two processes are used to manufacture the forged pieces used in the assembly of the wings of an airplane. Of 200 forged parts selected from process 1, 10 do not meet resistance specifications, while 300 forged parts selected from process 2, 20 are nonconforming. Build a confidence interval of 90% for the difference of the nonconforming fraction between the two processes ..

Answer 1

Sol:

p1^=sample proportion of defects of process1=10/200=0.05

p2^=sample proportion of defects of process2=20/300=0.06666667

Z alpha/2 for 90%=1.645

90% confidence interval for the difference of the nonconforming fraction between the two processes is

p1^-p2^+-zsqrt(p1^(1-p1^)/n1+p2^(1-p2^)/n2)

0.05-0.06666667+-1.645sqrt(0.05*(1-0.05)/200+0.066666678(1-0.06666667)/300)

=-0.01666667+-0.03469

=-0.01666667-0.03469,-0.01666667+0.03469

=-0.0514,0.0180

lower limit=-0.0514

upper limit=0.0180

we are 90% confident that the difference of the nonconforming fraction between the two processes lies in between -0.0514 and 0.0180