Photolithography plays a central role in manufacturing integrated circuits made
ID: 3126229 • Letter: P
Question
Photolithography plays a central role in manufacturing integrated circuits made on thin discs of silicon. Prior to a quality-improvement program, too many rework operations were required. In a sample of 200 units, 26 required reworking of the photolithographic step. Following training in the use of Pareto charts and other approaches to identify significant problems, a new sample of size 200 had only 12 that needed rework. Is this sufficient evidence to conclude at the 0.01 level of significance that the improvements have been effective in reducing the rework?
Explanation / Answer
Null, Ho: p1 = p2
Alternate,that the improvements have been effective in reducing the rework H1: p1 > p2
Test Statistic
Sample 1 : X1 =26, n1 =200, P1= X1/n1=0.13
Sample 2 : X2 =12, n2 =200, P2= X2/n2=0.06
Finding a P^ value For Proportion P^=(X1 + X2 ) / (n1+n2)
P^=0.095
Q^ Value For Proportion= 1-P^=0.905
we use Test Statistic (Z) = (P1-P2)/(P^Q^(1/n1+1/n2))
Zo =(0.13-0.06)/Sqrt((0.095*0.905(1/200+1/200))
Zo =2.387
| Zo | =2.387
Critical Value
The Value of |Z | at LOS 0.01% is 2.326
We got |Zo| =2.387 & | Z | =2.326
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value: Right Tail -Ha : ( P > 2.3873 ) = 0.00849
Hence Value of P0.01 > 0.00849,Here we Reject Ho
We have evidence that the improvements have been effective in reducing the rework