A production line operation is tested for filling weight accuracy using the following hypotheses.
Hypothesis Conclusion and Action
H0: μ = 16 .....Filling okay; keep running
Ha: μ ≠ 16 ..... Filling off standard; stop and adjust machine
The sample size is 30 and the population standard deviation is σ = .8. Use α = .05.
a. What would a Type II error mean in this situation?
b. What is the probability of making a Type II error when the machine is overfilling by .5 ounces?
c. What is the power of the statistical test when the machine is overfilling by .5 ounces?
d. Show the power curve for this hypothesis test. What information does it contain for the production manager?