A machine in a factory is supposed to fill vials with approximately 50mL of a liquid. The quality control manager wants to test whether the machine is working properly. If the machine is found to be over or under-filling then the assembly line will need to be shut down so that it can be re-calibrated.

a. State the Null and Alternative Hypotheses to the scenario using the correct symbols

b. What would it mean to make a Type 1 error in this situation?

c. What would it mean to make a Type 2 error in this situation?

d. Why might it be worse to make a Type 1 error in this scenario?

e. Suppose that we fail to reject the null hypothesis. Write a conclusion statement in the context of the problem. Assume no errors were made.