Question

1. 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.

Answer 1

Question 1

(a) Null Hypothesis : H₀ : The mean fill of liquid is 50 ml. = 50 mL

Alternative Hypothesis : H_a : The mean fil of liquied is not equal to 50 ml. 50 mL

(c) Here type I error means that we will reject the null hypothesis that means we will conclude that the mean fill in liquid is not equal to 50 ml when in reality it is 50 mL.

(c) Here type II error means that we will fail to reject the null hypothesis that means we will conclude that mean fill of liquid is equals to 50 ml when in reality it is not 50 ml.

(d) Here It is worse to make a type I error as if type I error occurs then whole assembly line has to be shut down for recaliberation when there is no such real case involved.

(e) Here as we fail to reject the null hypothesis we will conclude that there is no need for machine to recliberateed and machine is working fine.