Two machines produce computer memory chips Of 500 chips prod

Two machines produce computer memory chips. Of 500 chips produced by the first machine, 20 were defective; of 600 chips produced by the second machine, 40 were defective. Are the two machines equally reliable? Construct an interval appropriate to draw a conclusion with a level of significance of .02. Clearly outline your reasoning.

Solution

Null, There Is No Significance between them Ho: p1 = p2
Alternate, There Is Significance between them H1: p1 != p2
Test Statistic
Sample 1 : X1 =20, n1 =500, P1= X1/n1=0.04
Sample 2 : X2 =40, n2 =600, P2= X2/n2=0.067
Finding a P^ value For Proportion P^=(X1 + X2 ) / (n1+n2)
P^=0.055
Q^ Value For Proportion= 1-P^=0.945
we use Test Statistic (Z) = (P1-P2)/(P^Q^(1/n1+1/n2))
Zo =(0.04-0.067)/Sqrt((0.055*0.945(1/500+1/600))
Zo =-1.939
| Zo | =1.939
Critical Value
The Value of |Z | at LOS 0.02% is 2.326
We got |Zo| =1.939 & | Z | =2.326
Make Decision
Hence Value of |Zo | < | Z | and Here we Do not Reject Ho
P-Value: Two Tailed ( double the one tail ) -Ha : ( P != -1.9392 ) = 0.0525
Hence Value of P0.02 < 0.0525,Here We Do not Reject Ho