In the past our production line has had a defect rate of 4 I

In the past, our production line has had a defect rate of 4%. I wish to test whether that rate has changed. I sample 1000 units and find that 54 are defective. Construct a hypothesis test.

H0:

H1:

Test Statistic:

P-value Conclusion

Solution

Set Up Hypothesis
Null, H0:P=0.04
Alternate, H1: P!=0.04
Test Statistic
No. Of Success chances Observed (x)=54
Number of objects in a sample provided(n)=1000
No. Of Success Rate ( P )= x/n = 0.054
Success Probability ( Po )=0.04
Failure Probability ( Qo) = 0.96
we use Test Statistic (Z) for Single Proportion = P-Po/Sqrt(PoQo/n)
Zo=0.054-0.04/(Sqrt(0.0384)/1000)
Zo =2.2592
| Zo | =2.2592
P-Value: Two Tailed ( double the one tail ) - Ha : ( P != 2.25924 ) = 0.02387