#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.

#2 The proportion of Americans who have frequent migraines is 15.2% according to the CDC. An acupuncturist claims that her treatment can reduce this figure significantly. A random sample of 675 Americans is administered the acupuncturists treatment and 101 report experiencing migraines.
a. State Hypotheses to the scenario using the correct symbols.
b. What is the sample proportion? (Round to 2 decimal places) p^=
c. Suppose the P-value is calculated to be 0.0276 What would your decision be for this test using α=α= 0.05?
Would you:
-Accept the null, reject the null, or fail to reject the null