Question

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 overfilling or underfilling is occurring. If the sample data lead to a conclusion of overfilling or underfilling, 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.
d. What is the Type I error in this situation? What are the consequences of making this error?
e. What is the Type II error in this situation? What are the consequences of making this error?

I do NOT need the answers to a, b and c. I ONLY NEED the answers to d and e and PLEASE SHOW WORK.

Thanks!

Answer 1

Ans d: the type 1 error is the rejection of true null hypothesis. In this context it means to claim the carton are being underfilled or overfilled when in fact, they are not. The consequences of committing type 1 error is the loss of revenue and time which will happen when the production line will be shut down.

Ans e: The Type 2 error is the non rejection of false null hypothesis. In this context, it means to claim the cartons are not being underfilled or overfilled when in fact they are. The consequences of committing type 2 error is the condition of production line will deteriorate over time and they might have to discard the underfilled cartons and the raw materials will excessively consumed in case of overfilled cartons