Two extrusion machines that manufacture steel rods are being

Two extrusion machines that manufacture steel rods are being compared. In a sample of 1000 rods taken from machine 1, 960 met specifications regarding length and diameter. In a sample of 600 rods taken from machine 2, 582 met the specifications. Machine 2 is more expensive to run, so it is decided that machine 1 ill be used unless it can be convincingly shown that machine 2 produces a larger proportion of rods meeting specifications.

a) state the appropriate null and alternative hypotheses for maing the decision as to which machine to use

b) compute the p-value

c) which machine should be used?

Thank you!

Solution

Null Hypothesis, There Is No Significance between them Ho: p1 > p2
Alternate, Machine 2 is more expensive to run H1: p1 < p2
Test Statistic
Sample 1 : X1 =960, n1 =1000, P1= X1/n1=0.96
Sample 2 : X2 =582, n2 =600, P2= X2/n2=0.97
Finding a P^ value For Proportion P^=(X1 + X2 ) / (n1+n2)
P^=0.964
Q^ Value For Proportion= 1-P^=0.036
we use Test Statistic (Z) = (P1-P2)/(P^Q^(1/n1+1/n2))
Zo =(0.96-0.97)/Sqrt((0.964*0.036(1/1000+1/600))
Zo =-1.036
| Zo | =1.036
Critical Value
The Value of |Z | at LOS 0.05% is 1.645
We got |Zo| =1.036 & | Z | =1.645
Make Decision
Hence Value of |Zo | < | Z | and Here we Do not Reject Ho
P-Value: Left Tail - Ha : ( P < -1.036 ) = 0.15009
Hence Value of P0.05 < 0.15009,Here We Do not Reject Ho

There Is No Significance between them Machine 1, Machine 2