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...

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 four specimens.

(a) What is the type I error probability if the critical region is defined as kilograms?

(b) Find ß for the case where the true mean elongation is 11.25 kilograms.