A production line operation is designed to fill cartons with laundry detergent to a mean weight of 32 ounces. A sample of cartons is periodically selected and weighed to determine whether underfilling or overfilling is occurring. If the sample data lead to a conclusion of underfilling or overfilling, the production line will be shut down and adjusted to obtain proper filling.
a. Formulate the null and alternative hypotheses that will help in deciding whether to shut down and adjust the production line.
b. Comment on the conclusion and the decision when H0 cannot be rejected.
c. Comment on the conclusion and the decision when H0 can be rejected.
Condition
H0 True Ha True
Accept H0
Correct Type II
Conclusion Error
Conclusion
Reject H0
Type I Correct
Error Conclusion