Solution:-
- The population proportion, P = 0.03 ( 3 % )
- The sample proportion, p = 0.058 ( 5.8 % )]
- The sample size , n = 85.
- State the hypothesis:
Null hypothesis : P = 0.03 ( 3 % )
Alternate hypothesis : P ≥ 0.03 ( 3 % )
- The rejection region is defined by the significance level α:
significance α = 0.05
Z-critical = Z_α = Z_0.05
p-value = Z_0.05 = 1.645
- The Z-statistics:
- Compare against the rejection value ( p - value ):
Z-critical = 1.645
Z-test = 1.5132
Z-test < Z-critical ... ( Null not rejected )
- We fail to reject the Null hypothesis, there is not enough evidence to support the manager's claim that the production process is out of control. Hence, we can support that the production process is not out of control.