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 H_0: mu = 12 against H_1: mu < 12, using a random sample of four specimens. Round your answers to 4 decimal places.1. What is the type I error probability, if the critical region is defined as x < 11.5 kilograms?2. Find beta for the case where the true mean elongation is 11.26 kilograms.3. Find beta for the case where the true mean is 11.5 kilograms.