A textile fiber manufacturer is investigating a new drapery yarn, which the company claims has a mean thread elongation of 12 kilograms with a standard deviation of 0.5 kilograms. The company wishes to test the hypothesis against , using a random sample of 4 specimens.
a. What is the type I error probability if the critical region is defined as kilograms?
b. Find β for the case in which the true mean elongation is 11.25 kilograms.
c. Find β for the case in which the true mean is 11.5 kilograms.
Round your answers to 4 decimal places.